Electromagnetics in Medical Physics - tioh. Hee University Korea ... Gauss’ law...

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Transcript of Electromagnetics in Medical Physics - tioh. Hee University Korea ... Gauss’ law...

  • 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

    tioh@khu.ac.kr

    mailto:ejwoo@khu.ac.kr

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

    2

    Electricity

    www.kemco.co.kr

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

    3

    Atom and Charge

    C12

    6

    = +

    = =

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

    4

    Periodic Table of Elements

    : Daum

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

    5

    Property: Conductivity

    +

    Conductivity

    Insulator

    Proton

    Electron

    + +

    + + +-

    -

    -

    -

    -

    -

    Conductorvs.

    Conductivity

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

    6

    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

    7

    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

    8

    Coulombs 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

    9

    Coulombs 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

    10

    Induced Charge

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

    11

    ,

    : =1

    40

    12

    2

    1

    40 9 109Nm2C2

    where 0 = 8.85 10-12 C2/N.m2 is the permittivity constant.

    The ratio 1/40 is often replaced with the electrostatic constant (or Coulomb constant) k=8.99109 N.m2/C2. Thus k = 1/40 .

    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

    12

    Coulombs 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

    13

    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

    14

    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

    15

    Electric Flux ()

    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

    16

    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 d through a patch element with area vector dA

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

    17

    Flux through a Surface

    A S

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

    18

    Flux through a Surface

    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

    19

    Gauss Law

    Ch23, HRW, Fundamentals of Physics, Wiley

    Gauss law relates the net flux 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

    : =

    0=

    4

    40

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

    20

    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,

    = = 42 =

    0, =

    402

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

    21

    Applying Gauss Law: Cylindrical Symmetry

    Figure shows a section of an infinitely long cylindricalplastic rod with a uniform charge density . 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.

    () = , = (1)

    = 2 =

    0, =

    20, =

    1

    40

    2

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

    22

    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 . 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 A is the charge enclosed by the Gaussian surface. This gives

    Non-conducting Sheet

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

    23

    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 1. 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

    [ 6.11 ]

  • EOD