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65. (a) The electric potential is the sum of the contributions of the individual spheres. Let
q
1
be the charge on one,
q
2
be the charge on the other, and
d
be their separation. The point
halfway between them is the same distance
d
/2 (= 1.0 m) from the center of each sphere,
so the potential at the halfway point is
()
( )
92
2
8
8
2
12
8.99 10 N m C
1.0 10 C 3.0 10 C
1.8 10 V.
42
1
.
0
m
qq
V
d
ε
−−
×⋅
×−
×
+
==
=
−
×
0
π
(b) The distance from the center of one sphere to the surface of the other is
d – R
, where
R
is the radius of either sphere. The potential of either one of the spheres is due to the
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 Spring '08
 Any
 Physics, Charge, Electric Potential

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