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HW 8 Phys5405 f05 due 10/27/05
1) A homopolar generator of electric current consists of a solid, cylindrical metal disk of
moment of inertia I, inner radius
R
i
, and outer radius
R
o
that is free to rotate without
friction about an insulating cylindrical axle of radius
R
i
. The axle is directed along the z
axis and there is everywhere a constant magnetic ﬁeld
B
=
B
0
e
z
. Via brush contacts a load
resistance R at point a is connected to the disk at
R
i
and at point b on the other side of the
resistance to the disk at
R
o
. The disk is started with angular velocity
ω
0
e
z
and thereafter
there is no external force. Find a value for the current as a function of
ω
(t). Does the
current ﬂow fron
R
i
to
R
o
or visa versa? Show that the disk will slow down and ﬁnd an
expression for
ω
(
t
).
2a) Show that the 4vector potential
A
μ
is not unique, by showing the 4vector potential,
A
0
μ
=
A
μ
+
∂
Ψ
∂r
μ
, gives the same
F
μν
.
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 Spring '10
 Blecher
 Current, Magnetism, Friction, Inertia

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