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Princeton University—Physics 501
Problem Set 2
Due: October 4, 2011
1) A charge +
q
rests at the midpoint (
z
= 0) between two inﬁnite conducting planes,
which are separated by a distance 2
a
and held at zero potential. Find the potential
everywhere in the space between the plates.
2) A point charge
q
is at the center of a very long grounded conducting cylinder of radius
a
.
a) Find the potential inside and outside of the cylinder.
b) Calculate and plot the
~
E
ﬁeld inside the cylinder—i.e., plot
E
z
and
E
ρ
as functions
of
ρ
for
z
=
a/
2 and
z
=
a/
4.
Hint:
Treat the charge
q
as being spread over a small disc with surface charge density
σ
=
qδ
2
(
ρ
) where
δ
2
(
ρ
) is the twodimensional
δ
function deﬁned as
Z
∞
0
δ
2
(
ρ
)2
πρdρ
= 1
.
x
= 0
,y
= 0
,z
= 0 and
x
=
a,y
=
a,z
=
a
. The walls
z
= 0 and
z
=
a
are held at a
constant potential
V
. The other four sides are at zero potential.
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 '11
 MARLOW
 Charge, Magnetism

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