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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