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Electromagnetics in Medical Physics

Part I. Impulses in Nerve

Tong In Oh

Department of Biomedical Engineering

Impedance Imaging Research Center (IIRC)

Kyung Hee University

Korea

[email protected]

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Electricity

www.kemco.co.kr

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Atom and Charge

C12

6

원소기호

질량수= 양성자 수 + 중성자 수

원자번호= 양성자 수= 중성 원자의 전자 수

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Periodic Table of Elements

그림출처 : Daum 통합검색

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Property: Conductivity

+

Conductivity

Insulator

Proton

Electron

+ +

+ + +-

-

-

-

-

-

Conductorvs.

Conductivity

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Charged Particle and Charge Density

• Free electron and hole are mobile

• Unbounded ion and molecule are mobile

• Bounded atom and molecule are immobile but may vibrate

• Polar molecule has no net charge but dipole moment and may rotate

• Mass

• Charge

• Size

• Position , , ,m Q dr

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Electric Field

• Space with nothing

• Space with a single charged particle

• Space with two charged particles

Qx

y

z

0

Qrr

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Coulomb’s Law

(a) The two glass rods were each rubbed with a silk cloth and one was suspended by thread. When they are close to each other, they repel each other.

(b) The plastic rod was rubbed with fur. When brought close to the glass rod, the rods attract each other.

Ch21, HRW, Fundamentals of Physics, Wiley

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Coulomb’s Law

Ch21, HRW, Fundamentals of Physics, Wiley

(a) Two charged rods of the same sign repel each other.

(b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge.

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Induced Charge

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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쿨롱의법칙, 중첩

• 쿨롱의법칙: 𝐹 =1

4𝜋𝜀0

𝑞1𝑞2

𝑟2

•1

4𝜋𝜀0≈ 9 × 109Nm2C−2

where ε0 = 8.85 × 10-12 C2/N.m2 is the permittivity constant. The ratio 1/4πε0 is often replaced with the electrostatic constant (or Coulomb constant) k=8.99×109 N.m2/C2. Thus k = 1/4πε0 .

Multiple Forces: If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces.

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Coulomb’s Law

)8.4(|rr|

)rr(Q

4

Q

|rr|4

)rr(QQ

|rr|4

)rr(QQ

|rr|4

)rr(QQF

N

1k3

k

kk

0

3

N0

NN

3

20

22

3

10

11

Q

Q1

Q2

QN

Qk

rr1F

rr 2F

rr kF

rr NF

Source Points

Field Point

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Electric Field

The electric field E at any point is defined in terms of the electrostatic force F that would be exerted on a positive test charge q0 placed there:

Electric Field

Ch22, HRW, Fundamentals of Physics, Wiley

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Electric Field

)12.4(|rr|

)rr(Q

4

1

|rr|4

)rr(Q

|rr|4

)rr(Q

|rr|4

)rr(QE

N

1k3

k

kk

0

3

N0

NN

3

20

22

3

10

11

Q=1C

Q1

Q2

QN

Qk

rr1E

rr 2E

rr kE

rr NE

Source Points

Field Point

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Electric Flux (전기장의선속)

Ch23, HRW, Fundamentals of Physics, Wiley

Electric field vectors and field lines pierce an imaginary, spherical Gaussian surface that encloses a particle with charge +Q.

Now the enclosed particle has charge +2Q.

Can you tell what the enclosed charge is now?Answer: -0.5Q

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Electric Flux

Ch23, HRW, Fundamentals of Physics, Wiley

Now we can find the total flux by integrating the dot product over the full surface.The total flux through a surface is given by

The net flux through a closed surface (which is used in Gauss’ law) is given by

where the integration is carried out over the entire surface.

Electric flux dϕ through a patch element with area vector dA

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Flux through a Surface

A S

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Flux through a Surface

적분감싸서에서

적분에서

S Surface :

)14.3(SdA

S Surface :

)13.3(SdAdSaAdScos|A|

S

SS nS

Closed Surface

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Gauss’ Law

Ch23, HRW, Fundamentals of Physics, Wiley

Gauss’ law relates the net flux ϕ of an electric field through a closed surface (a Gaussian surface) to the net charge qenc that is enclosed by that surface. It tells us that

We can also write Gauss’ law as

Two charges, equal in magnitude but opposite in sign, and the field lines that represent their net electric field. Four Gaussian surfaces are shown in cross section.

S1: Positive, S2: Negative, S3: Zero(qenc = 0), S4:Zero

전기장의선속 : 𝐸𝑛𝑑𝑆 =𝑞

𝜀0=

4𝜋𝑞

4𝜋𝜀0

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Applying Gauss’ Law: Spherical Symmetry

A thin, uniformly charged, spherical shell with total charge q, in cross section. Two Gaussian surfaces S1 and S2 are also shown in cross section. Surface S2 encloses the shell, and S1 encloses only the empty interior of the shell.

In the figure, applying Gauss’ law to surface S2, for which r ≥ R, we would find that

And, applying Gauss’ law to surface S1, for which r < R,

점전하

𝐸𝑛𝑑𝑆 = 𝐸 𝑑𝑆 = 4𝜋𝑟2𝐸 =𝑞

𝜀0, 𝐸 =

𝑞

4𝜋𝜀0𝑟2

점전하의경우에대한쿨롱의법칙유도

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Applying Gauss’ Law: Cylindrical Symmetry

Figure shows a section of an infinitely long cylindricalplastic rod with a uniform charge density λ. The chargedistribution and the field have cylindrical symmetry. To find thefield at radius r, we enclose a section of the rod with a concentric Gaussian cylinder of radius r and height h.The net flux through the cylinder from Gauss’ Law reduces to

yielding

A Gaussian surface in the form of a closed cylinder surrounds a section of a very long, uniformly charged, cylindrical plastic rod.

세포막(직선전하)𝑑𝑞 = 𝜆𝑑𝑥 , 𝜆 =선전하밀도 (𝐶𝑚−1)

𝐸නන𝑑𝑆 = 2𝜋𝑟𝐿𝐸 =𝜆𝐿

𝜀0, 𝐸 =

𝜆

2𝜋𝜀0𝑟, 𝐸 =

1

4𝜋𝜀0

2𝜆

𝑟

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Applying Gauss’ Law: Planar Symmetry

Figure (a-b) shows a portion of a thin, infinite, non-conducting sheet with a uniform (positive) surface charge density σ. A sheet of thin plastic wrap, uniformly charged on one side, can serve as a simple model. Here,

Is simply EdA and thus Gauss’ Law,

becomes

where σA is the charge enclosed by the Gaussian surface. This gives

Non-conducting Sheet

Electromagnetics in Medical Physics, Kyung Hee Univ. Spring, 2018

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Applying Gauss’ Law: Planar Symmetry

Figure (a) shows a cross section of a thin, infinite conducting plate with excess positive charge. Figure (b) shows an identical plate with excess negative charge having the same magnitude of surface charge density σ1. Suppose we arrange for the plates of Figs. a and b to be close to each other and parallel (c).

Since the plates are conductors, when we bring them into this arrangement, the excess charge on one plate attracts the excess charge

Two conducting Plates

on the other plate, and all the excess charge moves onto the inner faces of the plates as in Fig.c. With twice as much charge now on each inner face, the electric field at any point between the plates has the magnitude

[교재그림 6.11 참조]

EOD