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Homework set 3
1.
Jackson problem 3.1 Please do
not
completely solve this problem.
Rather it is easier to split this
problem into a sum of two problems by superposition: one which is completely symmetric and one which is
antisymmetric.
•
What are these two problems?
•
What series of special functions would you use to solve for the potential?
•
What property of these polynomials are you exploiting by splitting this problem into two problems?
2.
For the example of a Sphere With a Speci±ed Potential presented in class (Sec. IA.2) a point charge is
now introduced along the polar axis a distance
d
from the center of the sphere, but the charge is also added
and redistributed on the sphere so as to maintain the above boundary condition. Now ±nd the potential for
all
a < r < d
.
3.
The surface of a nearly spherical conductor is speci±ed by
r
(
θ
) =
a
"
1 +
∞
X
l
=0
δ
l
P
l
(cos
θ
)
#
,
where
δ
l
¿
1.
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 Fall '11
 Electrodynamics
 Work

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