Chapter 3 1

OutlineReading: Livingston, Chapter 3

• Dielectric in an DC Electric Field• Dielectric in a Capacitor• Types of Polarization• Polarization: Microscopic to Macroscopic• Dielectric in an AC Electric Field• Relaxation Model• Resonance Model• Frequency Dependence of Dielectric Constant

Chapter 3 2

Dielectric (Insulator) in a DC Electric Field

2

Chapter 3 3

Capacitor: Dielectric (Insulator) in a DC Electric Field

Chapter 3 4

Types of Polarization

+ +++ ++

+ +++ ++

Chapter 3 5

Polarization: Microscopic to Macroscopic

+ +

Chapter 3 6

Example: Electronic Polarizability

The electronic polarizability of the Ar atom is 1.7 x 10-40 F-m2. What is the dielectric constant of solid Ar (below 84K)?

Chapter 3 7

Capacitor: Dielectric (Conductor) in a AC Electric Field

dtdVCI =

Real Dielectric Mat’l:

)1( −= roP εε X

tioe

ω−=XXti

oro eP ωεε −−= X)1( tioro ei

dtdPJ ωεωε −−−== X)1(

Ideal Dielectric Mat’l:

Chapter 3 8

Frequency Dependence of Dielectric Constant

Chapter 3 9

Relaxation Model: Orientational Polarization

+

Chapter 3 10

Relaxation Model: Orientational Polarization (cont.)

Chapter 3 11

Resonance Model: Electronic Polarization

11

tioeeeKx

dtdxm

dtxdm ωγ −−=−=++ XX2

2++

Chapter 3 12

Frequency Dependence of Dielectric Constant

Chapter 3 13

Lecture #3: Review Questions

1. What are the units of polarization?2. How does a dielectric material act in a DC electric field? And, in an

AC electric field?3. What are the units on the relative dielectric constant of a material?

What are the units on the dielectric constant?4. Does the stored charge in a capacitor increase or decrease when a

dielectric material is inserted between the plates?5. What are the units of capacitance?6. What are the 5 types of polarization? Which one can respond to

optical frequencies?7. What is the relaxation time of a dielectric material?8. At what frequency is the maximum loss for a material with

electronic polarization?

Chapter 3 14

Important Equationsti

oro eP ωεε −−= X)1(

dtdVCI =

CVQ =

dAC ε=

2

21 CVE =

χε

ε +=+= 11Xo

rP

o

er

Nεαε +=1

Xε=D

Xeqdp α==

'

"

tand

d

εεδ =

"'

1)0()( dd

r

dd i

iεε

ωτεωε +=−

=

22'

1)0(

r

dd τω

εε+

=

rr

dd ωτ

τωεε 22

"

1)0(

+=

( )[ ]( )[ ]22222

22

γωωωωγωω

+−+−−=

r

roo

miex X

2/1

=

mK

rω