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Electricity and Magnetism I (P331)
M. R. Shepherd
October 31, 2008
The moving capacitor
Today in lecture we worked out both the magnetic and electric pressures on the plate of a capacitor due to
the other plate. At the end of class I tried to qualitatively draw a connection to relativity. If we had just a
little more time I would have made this connection a little more quantitative. Let’s ﬁnish oﬀ the problem.
We showed that the magnetic pressure due to the upper plate on the lower plate is
repulsive
and has a
magnitude
±
±
±
±
F
A
±
±
±
±
=
μ
0
σ
2
v
2
2
,
(1)
here
σ
is the charged density and
v
is the velocity of the plates. At the same time the electric pressure due
to the lower plate on the upper plate is
attractive
and has a a magnitude
±
±
±
±
F
A
±
±
±
±
=
σ
2
2
±
0
.
(2)
Let’s assume that the plates have equal but opposite charges
±
q
. Then, we can write the
net upward force
on the lower plate as
F
=
q
2
2
±
0

q
2
v
2
μ
0
2
=
q
2
2
±
0
(
1

v
2
μ
0
±
0
)
.
(3)
Now, suppose that we have two observers. One observer is standing on the upper plate as the plates
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This note was uploaded on 01/20/2012 for the course PHYSICS 331 taught by Professor Staff during the Fall '09 term at Indiana.
 Fall '09
 STAFF
 Magnetism, Work

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