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33.
(a) The charge on every part of the ring is the same distance from any point
P
on the axis. This
distance is
r
=
√
z
2
+
R
2
,where
R
is the radius of the ring and
z
is the distance from the center of
the ring to
P
. The electric potential at
P
is
V
=
1
4
πε
0
Z
dq
r
=
1
4
πε
0
Z
dq
√
z
2
+
R
2
=
1
4
πε
0
1
√
z
2
+
R
2
Z
dq
=
1
4
πε
0
q
√
z
2
+
R
2
.
(b) The electric Feld is along the axis and its component is given by
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 Fall '08
 SPRUNGER
 Physics, Charge, Electric Potential

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