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Chapter 5
Electric Field in
Material Space
Part 2
3
Polarization(P) in Dielectrics
The application of E to the dielectric material
causes the flux density to be grater than it would
be in free space.
PED o
P is proportional to the applied electric field E
EP oe
Where is the electric susceptibility of the material
- Measure of how susceptible (or sensitive) a given
dielectric is to electric field.
e
4
er
ro
ro
roeo
oeoo
EED
EE
EEPED
1
)()1(
ypermitivit
ypermitivit
ypermitivit
r
o
of
of
relative
dielectric
space free
5
space free
dielectric
of
of
ypermitivit
ypermitivitypermitivitrelative
o
r
Dielectric constantor(relative permittivity) εr
Is the ratio of the permittivity of the dielectric to
that of free space.
ro
6
Dielectric Strength
Is the maximum electric field that a dielectric can
withstand without breakdown.
ro Dielectric Strength
E(V/m)εrMaterial
7.5M80Water(sea)
12M7Paper
25M2.5-8Wood
12M2.1Oil
3M1Air
7
A parallel plate capacitor with plate separation of2mm has 1kV voltage applied to its plate. If the space between the plate is filled withpolystyrene(εr=2.55)Find E,P
2
3
/ 86.6)500)(55.21()1(
/k 500102
1000
mCkEEP
mVd
VE
orooe
8
In a dielectric material Ex=5 V/m
and
Find (a) electric susceptibility (b) E (c) D
2/)43(10
1mncaaaP zyx
e
517.2)5(
)3(10
1
)( o
eoe EPa
zyx
o
zyx
oe
aaaaaaP
Eb 67.667.15)517.2(
)43(
10
1)(
2pC/m 3.1866.4678.139
)1()(
zyx
eororo
aaa
EEEEDc
9
In a slab of dielectric material for which ε =2.4εo, V=300z2 V
Find (a) D and ρv(b) P and ρpv
nC/m43.7
nC/m 43.7
)600()4.21()1()(
3
2
P
Za
aZEEPb
pv
z
zooroe
nC/m75.12
nC/m 75.12)600)(4.2(
600 )(
3
2
D
ZaaZED
aZVEa
v
zzo
z
10
A spherical dielectric shell with ε =εoεr for a<r<b and ε =εo for 0<r<a
If a charge Q is placed at center of the shell find:
Find (a) P for a<r<b(b) ρpv for a<r<b
2 2
o
o
o o2 2
o
2
( ) for a r b
4 4
4 4
11
4
( ) 0
r
r
r
pv
a
Q QD E
r r
D E P
Q QP D E
r r
QP
r
b P
11
Two point charges when located in free space exert a force of 4.5 μN on each other. When
the space between them is filled with a dielectric
material, the force changes to 2 μN. Find
the dielectric constant of the material
25.2102
105.4
2
1
4
21
4
21
2
1
6
6
r
r
2
ro
2
o
F
F
r
r
F
F
12
A conducting sphere of radius 10 cm is centered at
the origin and embedded in a dielectric
material with ε =2.5εo . If the sphere carries a surface
charge of 4 nC/m2,find E at (-3cm,4cm,12cm).
V/m 92.1065.2
10367.2
5.210367.2
))1.0(4())13.0(4(
13)12()4()3(
.
:law sGauss'
9
9
22
222
2222
o
o
s
sen
E
EED
D
cmr
zyxr
dSdSDQ
from
13
A sphereradius=a, εr ,uniform charge density of ρo.
(a) At the center of the sphere, show that
r
ro
o aε3ε
rρE
arfor (1)
ro
o
sen
ro
ar
D
rrD
dSdSDQ
dlEV
3
) 3
4() 4(
.
,
.
32
)12(6
2
r
ro
oaV
r2
o
3
o ar 3ε
aρE
arfor )(
ro
o
sen
o
ar
aD
arD
dSdSDQ
2
3
32
3
) 3
4() 4(
.
, 2
14
r
ro
o
o
o
ro
o
a o
o
a
ro
o
εεε
aρ
aε
aρ
εε
aρ
dr rε
aρdr
εε
rρE.dlV
216
]1
[36
33
2
32
2
3
0
(b) Find the potential at the surface of the sphere.
r
o
a o
o
ε
aρ
dr rε
aρE.dlV
3
3
2
2
3
