Physics 505
Fall 2007
Homework Assignment #8 — Due Thursday, November 8
Textbook problems: Ch. 5: 5.13, 5.14, 5.15, 5.16
5.13 A sphere of radius
a
carries a uniform surfacecharge distribution
σ
.
The sphere is
rotated about a diameter with constant angular velocity
ω
. Find the vector potential
and magneticflux density both inside and outside the sphere.
5.14 A long, hollow, right circular cylinder of inner (outer) radius
a
(
b
), and of relative
permeability
μ
r
, is placed in a region of initially uniform magneticflux density
~
B
0
at
right angles to the field. Find the flux density at all points in space, and sketch the
logarithm of the ratio of the magnitudes of
~
B
on the cylinder axis to
~
B
0
as a function
of log
10
μ
r
for
a
2
/b
2
= 0
.
5, 0
.
1. Neglect end effects.
5.15 Consider two long, straight wires, parallel to the
z
axis, spaced a distance
d
apart and
carrying currents
I
in opposite directions. Describe the magnetic field
~
H
in terms of
a magnetic scalar potential Φ
M
, with
~
H
=

~
∇
Φ
M
.
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 Fall '08
 Stephens,P
 Cartesian Coordinate System, Charge, Magnetism, Work, Magnetic Field

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