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76. The electric field at a point on the axis of a uniformly charged ring, a distance
z
from
the ring center, is given by
E
qz
zR
=
+
4
0
22
32
π
ε
c
h
/
where
q
is the charge on the ring and
R
is the radius of the ring (see Eq. 2216). For
q
positive, the field points upward at points above the ring and downward at points below
the ring. We take the positive direction to be upward. Then, the force acting on an
electron on the axis is
F
eqz
=−
+
4
0
π
c
h
/
.
For small amplitude oscillations
z
R
<<
and
z
can be neglected in the denominator. Thus,
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This note was uploaded on 07/10/2010 for the course PH 345 taught by Professor Vb during the Fall '10 term at The Petroleum Institute.
 Fall '10
 VB
 Charge

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