Electromagnetics
School of Electrical and Computer Engineering
University of Tehran
Supplementary Exercises 3
Fall Semester 1384
Problem 1
In free space, electric dipoles are uniformly distributed in the region
a
r
≤
≤
0
,
π
ϕ
2
0
≤
≤
,
h
z
≤
of the cylindrical coordinate system. The polarization vector in this region is given by
z
P
P
o
ˆ
=
r
where
o
P
is a known constant. (Note that this distribution can be realized with the help
of a cylindrical electret.)
a)
Determine
E
r
and
D
r
along the
z
axis.
b)
Plot qualitatively the
E
r
and
D
r
field lines for a
ϕ
constant plane.
Problem 2 (Griffiths: Problem 2.36)
Consider a spherical conductor of radius
R
as shown in the following figure. Inside the
conducting sphere, there are two spherical cavities of radius
1
R
and
2
R
. Two point charges
1
q
and
2
q
are placed in the center of the cavities.
a)
Find the surface charges on all surfaces.
b)
Find the field outside the conductor.
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 Spring '11
 Dolatabadi
 Electrostatics, Electromagnet, Electric charge, Electromagnetics School of Electrical and Computer Engineering University of Tehran, sufficient boundary condition

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