26
CHAPTER 15
(b) Note that the result of part (a) may be written as
( )
()
32
22
e
R
kQb
E
ab
=
+
where
Q
2
q
=
is
the total charge in the charge distribution generating the field.
In the case of a uniformly charged circular ring, consider the ring to consist of a
very large number of pairs of charges uniformly spaced around the ring. Each pair
consists of two identical charges located diametrically opposite each other on the
ring. The total charge of pair number
i
is
Q
. At a point on the axis of the ring, this
pair of charges generates an electric field contribution that is parallel to the axis and
has magnitude
i
ei
i
kbQ
=
+
E
.
The resultant electric field of the ring is the summation of the contributions by all
pairs of charges, or
2
ee
Ri
i
kb
EE
Q
=Σ
=
Σ
=
++

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