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Prof. David R. Jackson Dept. Of ECE Spring 2018 Notes 20 Dielectrics ECE 3318 Applied Electricity and Magnetism 1
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Transcript of Prof. David R. Jackson ECE Dept. - University of Houstoncourses.egr.uh.edu/ECE/ECE3318/Class...

  • Prof. David R. Jackson Dept. Of ECE

    Spring 2018

    Notes 20 Dielectrics

    ECE 3318 Applied Electricity and Magnetism

    1

  • Dielectrics

    Water

    0 r =

    Single H2O molecule:

    2

    +

    -

    H+

    O-

    H+ +

    http://en.wikipedia.org/wiki/File:H2O_2D_labelled.svg

  • Dielectrics (cont.)

    Water

    0 r =

    Dipole model: p p

    p qd

    =

    =

    Vector dipole moment of molecule p:

    3

    +

    -

    d

    q+

    q

    +

    -

    H+

    O-

    H+ +

  • Dielectrics (cont.)

    4

    The dipoles representing the water molecules are normally pointing in random directions.

    +

    + +

    -

    +

    -

    + -

    - -

    - +

    Note: The molecules are not floating in water they make up the water.

  • Dielectrics (cont.)

    5

    The dipoles partially align under an applied electric field.

    + -

    +

    +

    +

    +

    -

    -

    -

    -

    + -

    + -

    + -

    + -

    x

    0V

    xE

  • Define: P = total dipole moment/volume

    1i

    VP p

    V

    0D E P +

    Define the electric flux density vector D:

    V

    Dielectrics (cont.)

    We can also write this as

    ( )( )1 avei vV

    NP p N pV N

    = =

    pave = average vector dipole moment

    N molecules (dipoles) inside V

    6

    /vN N V= Nv = number of molecules per unit volume

  • Linear material: 0 eP E =

    Define:

    0 r =

    0 rD E =Then we have

    Note: e > 0 for most materials

    Dielectrics (cont.)

    The term e is called the electric susceptibility.

    ( )0 0

    0 1e

    e

    D E EE

    = +

    = +

    1r e +

    7

    D E=or where

    Note: A negative value of e

    would mean that the dipoles align against the field.

  • Typical Linear Materials

    Teflon Water Styrofoam Quartz

    2.2811.035

    r

    r

    r

    r

    ====

    (a very polar molecule, fairly free to rotate)

    8

    Note: r > 1 for most materials: 1 , 0r e e + >

  • Dielectrics: Bound Charge

    0vb = + +

    20

    :4

    qr b E rr

    > =

    From Gausss law:

    Example (cont.)

    0a bb bq q+ =

    b ab bq q= Note :

    where

    +

    + +

    +

    + +

    + +

    - -

    -

    -

    -

    -

    - -

    abq

    bbq

    q

    S

    r b>

  • 26

    Observations

    We get the correct answer by accounting for the bound charges, and putting them in free space.

    However, it is much easier to not worry about bound charges,

    and simply use the concept of r and the free charge.

    enclS

    D n dS Q =

    0 rD E E = =

    From the previous example, we have the following observations:

    Free charge enclosed

  • Exotic Materials

    27

    Plasmas have a relative permittivity that is less than one (and can even be negative)

    Plasmas

    2

    0 1p

    =

    ( )

    2

    0 1p

    j

    =

    Lossless plasma:

    Lossy plasma:

    p = plasma resonance frequency

    = plasma collision frequency (loss term)

    (derived in ECE 6340)

  • Exotic Materials (cont.)

    28

    Low frequencies (f < 30 MHz) will reflect off the ionosphere.

    Plasmas

    Shortwave radio signals propagate around the earth by

    skipping off the ionosphere.

    The ionosphere has a relative permittivity that is less than one, so the waves will bend (refract) away from the normal and

    travel back down to the earth, bouncing off of the earth.

    https://en.wikipedia.org/wiki/Skywave

  • Exotic Materials (cont.) Artificial metamaterials that have been designed that have

    exotic permittivity and/or permeability performance.

    29

    Negative index metamaterial array configuration, which was constructed of copper

    split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board.

    The total array consists of 3 by 2020 unit cells with overall dimensions of 10100100 mm.

    http://en.wikipedia.org/wiki/Mhttp://en.wikipedia.org/wiki/Metamaterialetamaterial

    00

    r

    r