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1. ECEG 2210
Electromagnetic Fields
Electric Fields in Material Space

2. • Introduction
• Properties of Materials
• Convection and Conduction Currents
• Conductors
• Polarization in Dielectrics
• Dielectric Constant and Strength
• Linear, Isotropic, and Homogeneous Dielectrics
Electric Fields in Material Space

3. • Theory of electric phenomena in material space
• Most formulas derived earlier are still applicable
(some may require modification)
• Just as electric fields can exist in free space, they can
exist in material media.
• Broad classification of materials: conductors and
nonconductors.
• Non-conducting materials are insulators or dielectrics.
Introduction

4. Why?
• an electron does not leave a conductor surface
• a current-carrying wire remains uncharged
• materials behave differently in an electric field
• waves travel with less speed in conductors than in
dielectrics
Knowledge to Electrical properties of materials answers it all
Properties of Materials

5. Properties of Materials (Cont’d)
• In a broad sense, materials may be classified in terms
of their conductivity in or (S/m)
• High conductivity (   1)  conductors (metals)
• Low conductivity ( 1)  insulators
• For conductivity in between  semiconductors
• Conductivity also depends on the temperature of the
metal
• At (T = 0°K), some conductors change to
superconductors
• major difference between metals and insulators is the
availability of electrons for conduction current

6. 6
Convection and Conduction Currents
dt
dQ
t
Q
I 



S)
J
(for 






 S
J
I
or
S
I
J n
n
Current Density:
Otherwise:
 





S
I
S
J
I dS
J
s,
thu
The current (in amperes) through a given area is the
electric charge passing through the area per unit time.
Current Densities:
convection current density (Ohm’s law doesn’t apply)
conduction current density, and
displacement current density

7. 7
y
v
v u
S
t
l
S
I 





 

y
v
y
S
I
u
J 




The y-directed current Jy is given by:
Consider the figure:
Convection and Conduction Currents (Cont’d)
In general:
u
J v


Where
I is the convection current and J is the convection current density in (A/m2).

8. Convection and Conduction Currents (Cont’d)
Conduction current requires a conductor,
characterized by free electrons that
provide conduction current.
E
F e


constant collision with the atomic lattice and
drifts from one atom to another moves the
electrons and from Newton’s Law:
E
u
e
m



Where:
m  electron mass
u  drift velocity
E  electric field
  average time interval
between collisions
For n electrons per
unit volume
ne
v 


Thus the conduction
current density is:
hm's Law
form of O
he po
known as t
m
ne
v int
2



 E
E
u
J 



9. 9
Conductors
A perfect conductor cannot contain an
electrostatic field within it. Why?
A conductor is an equipotential body!
E = - ∇V = 0.

10. 10
Consider the figure:






dS
E
dl
E

I
V
R
Conductors (Cont’d)
)
0
( 
 E
E
l
V
)
sec.
-
x
uniform
(
S
I

J
S
l
I
V
R
and
l
V
S
I







 E
J Ex. Show that the power,
2
R
I
P 

11. 11
Polarization in Dielectrics
• External electric field when applied to dielectrics displacement of charges
takes place
• The displacement of the charges result s in a polarized dipole
• The distorted charge distribution is equivalent, by the principle of
superposition, to the original distribution plus a dipole whose moment is
given by:
d
P Q

For N dipoles:
v
Q
N
k
k
k
v





 1
0
lim
d
P
Polarization of a nonpolar atom or molecule
Polarization of a polar molecule

12. 12
Polarization in Dielectrics(Cont’d)
P
E
D 
 0

The net effect of the dielectric on the electric field E is to increase D inside it by
amount P. In other words, due to the application of E to the dielectric material,
the flux density is greater than it would be in free space.
P would vary directly as the applied electric field E and for some dielectrics:
E
P 0

e

 
E
E
D
E
E
E
D














r
e
e
0
0
0
0 1

13. 13
 
E
E
D
E
E
E
D














r
e
e
0
0
0
0 1
Dielectric Constant and Strength
Then,
Where
r


 0

Where
0
)
1
(



 

 e
r
• The dielectric constant (or relative permittivity) r is the ratio of the
permittivity of the dielectric to that of the free space.
• The dielectric strength is the maximum electric field that a dielectric
can tolerate or withstand without breakdown

14. 14
Linear, Isotropic, and Homogeneous Dielectrics
A dielectric material (in which D = E) is linear if  does not change
with the applied E field. homogeneous if  does not change from point
to point, and isotropic if  does not change with direction.