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33. Consider an infinitesimal segment of the rod, located between
x
and
x + dx
. It has
length
dx
and contains charge
dq =
λ
dx = cx dx
. Its distance from
P
1
is
d + x
and the
potential it creates at
P
1
is
dV
dq
dx
cx dx
=
+
=
+
1
4
1
4
00
ππ
εε
.
To find the total potential at
P
1
, we integrate over the length of the rod and obtain
0
0
0
92
2
1
2
2
2
[l
n
()
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 Fall '10
 BG
 Physics, Charge

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