Section 4 2 TRƯỜNG ĐIỆN TỪ

4 2 Dielectrics Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C Jo[.]

Introduction to Electromagnetic Fields,

to supplement “Elements of Engineering

Electromagnetics, Sixth Edition”

by

Nannapaneni Narayana Rao

Edward C Jordan Professor of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

4.2 Dielectrics

are based upon the property of polarization, which is the phenomenon of the creation of electric dipoles within the material

Electronic polarization: (bound electrons are displaced to form a dipole)

- Q

d

+

-+

-Dipole moment

p = Qd

Orientational polarization: (Already existing dipoles are acted upon by a torque)

Ionic polarization: (separation of positive and negative ions

in molecules)

Direction into the paper

-+

- QE

q

q

QE

E d

Torque  QEd sin q

Q

 



T d × E

p × E

-+

-+

-+

-+

-+

-+

-+

-+

-+

-+

-+

-The phenomenon of polarization results in a polarization

charge in the material which produces a secondary E.

- rS0

-+ -+ -+ -+ -+ -+ -+

-z = d

z = 0

rS0

Ea

0

e e

  

0

pS pS

r  r

0

pS pS

r - r

-z = 0

z = d

S

E

-+ -+ -+ -+ -+ -+ -+

- - - - Et

- - -

-t

E

Polarization Current

displacement flux density vector, D, as

vary with the material, implicitly taking into account the effect of polarization

= permittivity, F m = relative permittivity

r





and

r

0

0 0

0

0

2

1

C m

e e r



 



 





D E P

= E

As an example, consider

Then, inside the material, 0 0  

0

0

S

z

S z

r



-

a

-+ -+ -+ -+ -+ -+ -+

- - -

-0

S

r

-0

S

r

z = d

z = 0

z



For 0 < z < d,

(a) D  rS0az  10-6az C m2

-+ -+ -+ -+ -+ -+ -+

- - - - z = d

z = 0

z

0

4

-2

0

6 9

1 10 4

4 10

z

z

z

 





- -





D

a a

0

z





a

Anisotropic Dielectrics:

D is not parallel to E in general Only for certain directions

(or polarizations) of E is D parallel to E These are known

as characteristic polarizations

















D is parallel to E for all E.

y

x

D E

x

D E

xx xy xz

     

(a) E  E0 za

x y

z

D D

E D



             

 

9  E z 9 

0

  8 2 0 2 5 0

0 0 9

(b) E  E0  ax - 2 ay 

x y z

D

             

 

4  E x 2 y 4 

0

eff reff

x y z

D

        

 

0

9 , 9

eff reff

E

9  E 2 x y 9 