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23.25.
I
DENTIFY
:
For a point charge,
kq
V
r
=
. The total potential at any point is the algebraic sum of the
potentials of the two charges.
S
ET
U
P
:
(a)
The positions of the two charges are shown in Figure 23.25a.
Figure 23.25a
(b)
2
(
)
:
.
(
)
kq
kq
kq x
a
x
a V
x
x
a
x x
a

+
=

=


2
(3
)
0
:
.
(
)
kq
kq
kq x
a
x
a V
x
a
x
x x
a

< <
=

=


2
(
)
0:
.
(
)
kq
kq
kq x
a
x
V
x
x
a
x x
a

+
<
=
+
=


A general expression valid for any
y
is
2
 


q
q
V
k
x
x a
=


.
(c)
The potential is zero at
and /3.
x
a
a
= 
(d)
The graph of
V
versus
x
is sketched in Figure 23.25b.
Figure 23.25b
E
VALUATE
:
(e)
For
2
:
,
kqx
kq
x
a V
x
x


≈
=
which is the same as the potential of a point
charge –
q
. Far from the two charges they appear to be a point charge with a charge that is
the algebraic sum of their two charges.
23.28.
I
DENTIFY
:
For a point charge,
2
k q
E
r
=
and
kq
V
r
=
.
S
ET
U
P
:
The electric field is directed toward a negative charge and away from a positive charge.
E
XECUTE
:
(a)
0
V
so
0
q
.
2
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 Fall '10
 dfs
 Charge

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