Electricity and Magnetism I (P331)
Homework 4
Due: Wednesday, October 7, 4:00 PM
1. Two semiinfinite conducting planes meet at at a 60
◦
angle. A charge +
q
is placed in the narrow gap
between the planes along the bisector of the 60
◦
angle. Assuming you want to compute the potential
in this region sketch the location
and magnitude
of all of the necessary image charges. (You do not
need to compute the potential.)
2. Two semiinfinite conducting planes meet at a 90
◦
angle. A charge +
q
is placed a distance
d
from each
plane.
(a) Compute the potential in the region in between the planes.
(b) How much work is required to move the charge from infinity to its location in between the planes?
3. Study the image charge problem discussed in Example 3.2 in your text (p. 124).
(a) Show that Equation 3.17 can be written as
V
(
r, θ
) =
1
4
π
0
q
√
r
2
+
a
2

2
ra
cos
θ

q
R
2
+ (
ra/R
)
2

2
ra
cos
θ
.
(1)
This form should make it clear that when
r
=
R
,
V
= 0.
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 Fall '09
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 Charge, Electrostatics, Magnetism, Work, Relaxation technique, Electric charge, semiinﬁnite conducting planes

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