P
Physics 4321
Homework Set 11
November 17, 2008
Due: November 24, 2008
1. A circular loop of wire with radius
R
lies in the
x

y
plane, centered at the origin.
If it carries a
current
I
, counterclockwise as viewed from the point
z
= +
R
z
^
, (a) what is its magnetic dipole
moment
m
?
(b) Using the values of
m
from part (a), calculate the approximate
B
field at points
far from the loop.
(c) For points on the
z
axis, show that your results are consistent with those
from the exact field in example 5.6 when
z
>>
R
.
2. Consider the motion of a particle with mass
m
and electric charge
q
e
in the field of a
hypothetical magnetic monopole
q
m
at the origin where
B
= (
µ
o
q
m
/4
π
r
2
)
r
^
.
(a) Find the
acceleration of the particle, expressing your answer in terms of
q
e
,
q
m
,
m
,
r
, and
v
, where
r
and
v
are the particle’s position and velocity, respectively.
(b) Show that the speed
v
=
v
is a
constant of the motion.
3. An infinitely long circular cylinder carries a uniform magnetization
M
parallel to its axis,
which is assumed to be parallel to
z
^
.
Find the magnetic field inside and outside the cylinder.
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 Fall '10
 LOWELLWOOD
 Current, Work, Magnetic Field, long circular cylinder, infinitely long cylinder, bound current densities

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