Physics 505
Fall 2007
Homework Assignment #5 — Due Thursday, October 11
Textbook problems: Ch. 3: 3.13, 3.17, 3.26, 3.27
3.13 Solve for the potential in Problem 3.1, using the appropriate Green function obtained
in the text, and verify that the answer obtained in this way agrees with the direct
solution from the differential equation.
3.17 The Dirichlet Green function for the unbounded space between the planes at
z
= 0
and
z
=
L
allows discussion of a point charge or a distribution of charge between
parallel conducting planes held at zero potential.
a
) Using cylindrical coordinates show that one form of the Green function is
G
(
~x, ~x
0
)
=
4
L
∞
X
n
=1
∞
X
m
=
∞
e
im
(
φ

φ
0
)
sin
nπz
L
sin
nπz
0
L
I
m
nπ
L
ρ
<
K
m
nπ
L
ρ
>
b
) Show that an alternative form of the Green function is
G
(
~x, ~x
0
) = 2
∞
X
m
=
∞
Z
∞
0
dk e
im
(
φ

φ
0
)
J
m
(
kρ
)
J
m
(
kρ
0
)
sinh(
kz
<
) sinh[
k
(
L

z
>
)]
sinh(
kL
)
3.26 Consider the Green function appropriate for Neumann boundary conditions for the
volume
V
between the concentric spherical surfaces defined by
r
=
a
and
r
=
b
,
a < b
.
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 Fall '08
 Stephens,P
 Magnetism, Work, 1 m, 1 L, φ, 0 l, Neumann boundary condition

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