Physics 4321
Homework Set 12
November 24, 2008
Due: December 1, 2008
1. If
J
f
= 0 everywhere, curl
H
= 0 everywhere, and then we can express
H
as
H
= grad W,
where W is a scalar potential.
Use Eq. (6.23) to show that
∇
2
W = (div
M
).
Note that this is a
Poissonlike equation with div
M
as the source.
Therefore, if div
M
= 0, we recover Laplace’s
equation and all the machinery we developed earlier with the electric potential.
2. A coaxial cable consist of two very thin, concentric conducting tubes, with the
inner tube carrying current into the page and the outer tube out of the page.
In each
tube, the current is uniformly distributed over the surface.
The region between the
tubes is filled with a material whose susceptibility is
χ
m
.
Calculate
B
,
H
,
M
,
J
b
, and
K
b
between the tubes.
The radius of the inner tube is
a
and that of the outer tube is
b
.
3. A current
I
exists in a long, straight wire having radius
a
.
The wire is made from a linear
magnetic material whose susceptibility is
χ
m
.
The current is distributed uniformly throughout
the wire.
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 Fall '10
 LOWELLWOOD
 Work, Magnetic Field, inner tube, long cylindrical solenoid, outer tube, Mumetal, concentric conducting tubes

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