35. (a) According to the result of problem 28, the electric potential at a point with coordinate
x
is given
by
V
=
Q
4
πε
0
L
ln
µ
x
−
L
x
¶
.
We diFerentiate the potential with respect to
x
to ±nd the
x
component of the electric ±eld:
E
x
=
−
∂V
∂x
=
−
Q
4
πε
0
L
∂
∂x
ln
µ
x
−
L
x
¶
=
−
Q
4
πε
0
L
x
x
−
L
µ
1
x
−
x
−
L
x
2
¶
=
−
Q
4
πε
0
x
(
x
−
L
)
.
At
x
=
−
d
we obtain
E
x
=
−
Q
4
πε
0
d
(
d
+
L
)
.
(b) Consider two points an equal in±nitesimal distance on either side of P
1
, along a line that is per
pendicular to the
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Electric Potential

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