Fundamentals of Magnetism - CBPFieeemag/lectures/Jander_I.pdf · Orbital Magnetic Moment •For an...

Fundamentals of Magnetism Albrecht Jander

Oregon State University

Part I H M B χ micro Part II M(H)

Magnetic Field from Current in a Wire

Amperersquos Circuital Law

119867 ∙ 119889119897 = 119868

Biot-Savart Law

119867 = 1198682120587120587

[Am]

119889119867 =119868119889119897 times 119877

4120587 1198772

I

H

c

c dl

dl

R r

c

Andreacute-Marie Ampegravere (1775ndash1836)

Jean-Baptiste Biot (1774 ndash1862)

Feacutelix Savart (1791 ndash 1841)

Magnetic Field from Current Loop

Use Biot-Savart Law

119867 = 1198682120587

[Am] 119889119867 =

119868119889119897 times 119877

4120587 1198772

I

H

r

In the center

Magnetic Field in a Long Solenoid

119867 = 119873119868119871

[Am]

I

H

Inside field is uniform with

I

L

N turns

JS

119867 = 119869119878 [Am]

Magnetic Field from ldquoSmallrdquo Loop (Dipole)

I

H

r

Magnetic Field from Small Loop (Dipole)

H

For R gtgt r

119867 =119868119868

41205871198773 2119955 cos 120579 + 120637sin (120579)

R

θ

119898 = 119868119868 [Am2] Magnetic (dipole) moment

[Am]

Compare to Electric dipole

Magnetic Field of a Dipole

H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898

Magnetic Poles and Dipoles

119867 =119902119898

41205871198772 [Am]

+ qm

Magnetic field from a magnetic ldquomonopolerdquo

[Am] 119902119898

+ q

119863 =119902

41205871198772

Electric charge Magnetic charge or ldquopolerdquo

d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898

Orbital Magnetic Moment

bullFor an electron with charge qe orbiting at a radius R with frequency f the Orbital Magnetic Moment is

bull It also has an Orbital Angular Momentum

bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2

bullElectrons orbiting a nucleus are like a circulating current producing a magnetic field

[Am2]

bullBohr Model orbit must be integer number of wavelengths

bull Thus the orbital magnetic moment is quantized

bull Magnetic moment restricted to multiples of

vmh

edB =λ

Bohr model of the atom

RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton

bullDeBroglie wavelength is

e-

dBλ

R

Louis de Broglie (1892-1987)

Orbital Moment is Quantized

Spin

Pauli and Bohr contemplate the ldquospinrdquo of a tippy-top

bull Spin is a property of subatomic particles (just like charge or mass)

bull A particle with spin has a magnetic dipole moment and angular momentum

bull Spin may be thought of conceptually as arising from a spinning sphere of charge (However note that neutrons also have spin but no charge)

Electron Spin bull When measured in a particular direction the

measured angular momentum of an electron is

2

plusmn=zL

bull When measured in a particular direction the measured magnetic moment of an electron is

Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=

Compare Spin Orbital

Bzm microplusmn= Bz Nm micro=bull We say ldquospin uprdquo and ldquospin downrdquo

e

e

mqg

Lm

2minus

= 1=g2=g

Stern-Gerlach Experiment - 1922

Walter Gerlach (1889-1979)

Otto Stern (1888-1969)

Demonstrated that magnetic moment is quantized with plusmnmicroB

Walther Gerlach Otto Stern (1922) Das magnetische Moment des Silberatoms Zeitschrift fuumlr Physik A Hadrons and Nuclei 9

Stern-Gerlach Experiment

Quantum Numbers of Electron Orbitals bullElectrons bound to a nucleus move in orbits identified by quantum numbers (from solution of Schroumldingers equation)

n 1hellip principal quantum number identifies the ldquoshellrdquo l 0n-1 angular momentum q type of orbital eg spdf ml -ll magnetic quantum number ms +frac12 or -frac12 spin quantum number

For example the electron orbiting the hydrogen nucleus (in the ground state) has

n=1 l=0 ml=0 ms=+frac12

In spectroscopic notation 1s1

Spectroscopic notation l=0 s l=1 p l=2 d l=3 f n l of electrons in orbital 1s22s2

Spin and Orbital Magnetic Moment bull Total orbital magnetic moment (sum over all electron orbitals)

bull Total spin magnetic moment

Eg Iron

1s22s22p63s23p63d64s2

How to fill remaining d orbitals (l=2) 6 electrons for 10 spots

full orbitals no net moment

sum= lmm Borbitaltot micro_

sum= sBspintot mm micro2_

ml=-2 ml=-1 ml=0 ml=+1 ml=+2 ms=+frac12 ms=-frac12

BspintotBorbitaltot mm micromicro 42 __ ==

Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M

Atomic magnetic moment

[Am2]

Atomic density

[1m3]

Magnetic moment per unit volume

[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here

M Object magnetic moment

119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Equivalent Loop Currents

What is H here

119868

M Atomic magnetic moment

[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868

Object magnetic moment

119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Equivalent Surface Current

Equivalent surface current

[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Equivalent Surface Pole Density

Magnetic pole density

[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886

Surface charge density

[Am]

[m2]

Atomic magnetic moment Atomic magnetic moment

[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Example NdFeB Cylinder

M

M =106 [Am]

vol ≃ 14middot10-6

2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]

A ≃ 7middot10-4 [m2]

JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +

Result is the same external to magnetic material

Hint we are ldquofarrdquo away from the dipoles


M

+ + + + + + + + + + + + +

Result is different inside the magnetic material

The Constitutive Relation

119913 = 120641120782(119919 + 119924)

Note in vacuum M is zero

B = Magnetic flux density [ Tesla ] H = Magnetic field ldquoMagnetizing forcerdquo [Am] M = Magnetization [Am] micro0 = Magnetic constant ldquoPermeability of free spacerdquo [Tesla-mA] [Henrym] [NA2]

119913 = 120641120782119919

What is microo

The ampere is that constant current which if maintained in two straight parallel conductors of infinite length of negligible circular cross section and placed 1 meter apart in vacuum would produce between these conductors a force equal to 2times10minus7 newton per meter of length

micro0 comes from the SI definition of the Ampere

I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B

Maxwellrsquos Equations (Magnetostatics)

120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920

Differential form Integral form

119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With

Magnetic charge density ie magnetic chargevolume


+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2

The perpendicular component of B is continuous across a boundary

H1|| H2||

The transverse component of H is continuous across a boundary (unless there is a true current on the boundary)

Demagnetizing Fields

+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M

119919119941 = minus119925119924 Demagnetizing Factor

Demagnetizing Factors Special Cases 119919119941 = minus119925119924 119925119961 + 119925119962 + 119925119963 = 120783

Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z

Demagnetizing Factors

119919119941 = minus119925119924

ldquoDemagrdquo fields in ellipsoids of revolution are uniform

119925119961 + 119925119962 + 119925119963 = 120783

Example Ba-Ferrite Sphere

119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]

Example Ba-Ferrite Ellipsoid

119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]

Susceptibility and Permeability Ideal permanent magnet

Ideal linear soft magnetic material

Real useful magnetic material

H

M

H

M

H

M

119924 = 120652119919 Susceptibility [unitless]

119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919

119913 = 120641120782120641119955119919 Rel Permeability

[unitless]

Example Long Rod in a Long Solenoid

119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]

Note without the rod

Example Soft Magnetic Ball in a Field

M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785

Example Thin Film in a Field

119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why

Torque and Zeeman Energy

+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861

Self Energy and Shape Anisotropy

119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M

Hd Higher energy Lower energy

ldquoShape Anisotropyrdquo

119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920

Assuming flux is uniform and contained inside permeable material

119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949

120641119912 Magneto-motive force ldquoMMFrdquo

Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944

Solve using electric circuit theory

Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924

B [Gauss] H [Oersted] M [emucc] 4πM [Gauss]

B [Tesla] H [Am] M [Am]

119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism

BD Cullity Introduction to Magnetic Materials Wiley-IEEE Press 2010 (revised version with CD Graham) M Coey Magnetism and Magnetic Materials Cambridge University Press 2010 S Chikazumi Physics of Magnetism John Wiley and Sons 1984 RC OrsquoHandley Modern Magnetic Materials John Wiley amp Sons 2000 RL Comstock Introduction to Magnetism and Magnetic Recording John Wiley amp Sons 1999 D Jiles Introduction to Magnetism and Magnetic Materials CRC Press 1998 Bozorth Ferromagnetism1951 (reprinted by IEEE Press 1993)

Fundamentals of Magnetism












Spin

Electron Spin



Quantum Numbers of Electron Orbitals

Spin and Orbital Magnetic Moment

Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions


Demagnetizing Factors Special Cases





Susceptibility and Permeability







Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


Amperersquos Circuital Law

119867 ∙ 119889119897 = 119868

Biot-Savart Law

119867 = 1198682120587120587

[Am]

119889119867 =119868119889119897 times 119877

4120587 1198772

I

H

c

c dl

dl

R r

c

Andreacute-Marie Ampegravere (1775ndash1836)

Jean-Baptiste Biot (1774 ndash1862)

Feacutelix Savart (1791 ndash 1841)


Use Biot-Savart Law

119867 = 1198682120587

[Am] 119889119867 =

119868119889119897 times 119877

4120587 1198772

I

H

r

In the center


119867 = 119873119868119871

[Am]

I

H


I

L

N turns

JS

119867 = 119869119878 [Am]


I

H

r


H

For R gtgt r

119867 =119868119868

41205871198773 2119955 cos 120579 + 120637sin (120579)

R

θ


[Am]



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


Use Biot-Savart Law

119867 = 1198682120587

[Am] 119889119867 =

119868119889119897 times 119877

4120587 1198772

I

H

r

In the center


119867 = 119873119868119871

[Am]

I

H


I

L

N turns

JS

119867 = 119869119878 [Am]


I

H

r


H

For R gtgt r

119867 =119868119868

41205871198773 2119955 cos 120579 + 120637sin (120579)

R

θ


[Am]



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119867 = 119873119868119871

[Am]

I

H


I

L

N turns

JS

119867 = 119869119878 [Am]


I

H

r


H

For R gtgt r

119867 =119868119868

41205871198773 2119955 cos 120579 + 120637sin (120579)

R

θ


[Am]



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


I

H

r


H

For R gtgt r

119867 =119868119868

41205871198773 2119955 cos 120579 + 120637sin (120579)

R

θ


[Am]



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


H

For R gtgt r

119867 =119868119868

41205871198773 2119955 cos 120579 + 120637sin (120579)

R

θ


[Am]



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119867 =119902119898

41205871198772 [Am]

+ qm


[Am] 119902119898

+ q

119863 =119902

41205871198772


d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

d

+ qm

qm

[Am] 119902119898



H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


H

For R gtgt r

119867 =11990211989811988941205871198773 2 cos 120579 + 120579sin (120579)

R

θ


[Am]

[Am] 119902119898




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism




bull Note

e-

2RfqIAm e πminus==

RRfmvRmL ee π2==

ratioicgyromagnetmq

Lm

e

e =minus

=2


[Am2]




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism




vmh

edB =λ


RfmhN

vmhNNR

eedB π

λπ2

2 ===

e

e

e

ee m

qNmqhNRfqm

2222

==minus=π

π

][10274292

224 Ammq

e

eB

minustimes==micro

Bohr Magneton


e-

dBλ

R



Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Spin







2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism



2

plusmn=zL


Be

ezz m

qsm microplusmn==

e

e

mq

Lm minus

=bull Note

e

e

mq

Lm minus

=e

e

mq

Lm

2minus

=



e

e

mqg

Lm

2minus

= 1=g2=g















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism















Eg Iron

1s22s22p63s23p63d64s2







Hundrsquos rules

Maximize Σms

Then maximize Σml

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Magnetization M


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898

What is H here


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


What is H here

119868


[Am2]

Atomic density

[1m3]


[Am] 119872 ≝119898119900119900119900

119907119907119897= 119898119886119886119900119898119889

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

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Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism



[Am] 119869119878 = 119872 times 119899

What is H here

119868

M 119899

JS [Am]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = I119868


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Magnetic Pole Model



[Am] 119872 ≝119898

119907119907119897

What is H here


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism



[Am] 120588119898119898 = 119872 ∙ 119899

M

120588119898119898 =119902119898

119886119903119886119886


[Am]

[m2]


[Am2]

Atomic density

[1m3]

119898119886119886119907119898 = 119902119898119889


119898119900119900119900 = sum119898119886119886119900119898 [Am2]

119889 =119873

119907119907119897


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

JS =106 [Am]

I = 20000 [A]

m = IA = 14 [Am2]


JS

A


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


M

M =106 [Am]


2 cm

3 cm

[m3]

m = 14 [Am2]

ρms =106 [Am]

qm = 700 [Am]

m = qmd = 14 [Am2]


ρms

d =2middot10-2 [m]

+ + + + + + + + + + + + +


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


M

+ + + + + + + + + + + + +




M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


M

+ + + + + + + + + + + + +



119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119913 = 120641120782(119919 + 119924)



119913 = 120641120782119919

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

What is microo



I1

I2

F

119913 = 120641120782119919 =120641120782119920120783 120784120645119955

119917 = 119920120784119923 times 119913 B


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


120513 ∙ 119913 = 120782

120513 times 119919 =

119913 ∙ 119941119956 = 120782

119919 ∙ 119941119949 = 119920


119913 = 120641120782(119919 + 119924)

120513 ∙ 119913 = 120641120782(120513 ∙ 119919 + 120513 ∙ 119924) 120513 ∙ 119919 = minus120513 ∙ 119924 = 120646119950 [Am2]

With



+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


+ + + + + + + + + + + + +

B H 119913 = 120641120782(119919 + 119924)

M

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Boundary Conditions

B1 B2


H1|| H2||



+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


+ + + + + + + + + + + + +

Hd

119919119941 prop 119924

M



Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


Sphere

119925119961 = 119925119962 = 119925119963 =120783120785

Long Rod

119925119961 = 119925119962 =120783120784

119925119963 = 120782

Thin Sheet

119925119961 = 119925119962 = 120782 119925119963 = 120783

x

y

z


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119919119941 = minus119925119924


119925119961 + 119925119962 + 119925119963 = 120783


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119919119941 = minus119925119924

119925119961 = 119925119962 = 119925119963 =120783120785

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120782 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120782120782 ) [kAm]

119913 = 120782 120783120784120783 [Tesla]


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119919119941 = minus119925119924

119925119961 = 119925119962 = 120782 120786120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120788 120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120790120784 120783 ) [kAm]

119913 = 120782 120783120782120786 [Tesla]


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119919119941 = minus119925119924

119925119963 = 120782 120783

Barrium Ferrite

119924~120783120783120782 [kAm]

119919119941 = minus120783120783 [kAm]

M H B

119913 = 120641120782(119919 + 119924)

119913 = 120641120782(120783120785120783 ) [kAm]

119913 = 120782 120783120788 [Tesla]




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism




H

M

H

M

H

M


119913 = 120641120782(119919 + 120652119919)

119913 = 120641120782(120783 + 120652)119919


[unitless]


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119867 = 119873119868119871

= 1 [kAm]

119872 = 120594119867 = 120594 119873119868119871

= 999 [kAm]

I =1 A NL = 1000m

120583120587 = 1000 120594 = 999

119861 = 1205830 119867 + 119872 = 1205830(1000kAm)= 125 [Tesla]

or

119861 = 1205830120583120587119867= 125 [Tesla]

119861 = 1205830119867= 000125 [Tesla]



M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


M Hd B

119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

Hext

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


B 119924 = 120652119919 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119925119924

119924 =120652

120783 + 119925120652119919119942119961119942 120652119942119942119942 =

120652120783 + 119925120652

lt 120785


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119924 = 120652119919119946119946119956119946119941119942 = 120652 119919119942119961119942 + 119919119941 = 120652 119919119942119961119942 minus 119924

Hext

119924 =120652

120783 + 120652119919119942119961119942

119919119946119946119956119946119941119942 =120783

120783 + 120652119919119942119961119942 119913119946119946119956119946119941119942 = 119861119942119961119942

Why


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


+ + + + + + + + + + + + +

F

F

M B = 119902119898119861

119983 = 119898 times 119861

Force

Torque

Energy

119864 = minus119898 ∙ 119861


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism


119864 = 12 1205830119872 ∙ 119867119889119907

119907119900119900

M Hd M



119864 = 121205830119872119898

2 119873119909 minus 119873119884 1199041199041198992(120579)

θ

E

0 180 360

M Easy axis

Har

d ax

is

Easy Easy

Hard Hard

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Magnetic Circuits

N turns

I 119919 ∙ 119941119949 = 119925119920


119913 = 120641120782120641119955119919 =120659119912

areaA

119925119920 = 120659120659

120659 =119949


Flux

Reluctance

path length l

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Magnetic Circuits

NI 120659119944119944119944 120659120785

120659120783 120659120784

120659120786 120659120783

120659119944119944119944


Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

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Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Units Confusion

119913 = 120641120782 119919 + 119924 119913 = 119919 + 120786120645119924



119913 ∙ 119919 [dynecm3] 119913 ∙ 119919 [Jm3]

119925119961 + 119925119962 + 119925119963 = 120783 119925119961 + 119925119962 + 119925119963 = 120786120645

CGS Units SI Units

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Books on Magnetism














Spin

Electron Spin





Slide Number 26

Magnetization M



Magnetic Pole Model







What is mo



Boundary Conditions














Magnetic Circuits

Magnetic Circuits

Units Confusion

Books on Magnetism

Fundamentals of Magnetism - CBPFieeemag/lectures/Jander_I.pdf · Orbital Magnetic Moment •For an...

Documents

Transcript of Fundamentals of Magnetism - CBPFieeemag/lectures/Jander_I.pdf · Orbital Magnetic Moment •For an...