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Figure 10: Three charged particles.
Recall that the potential is related to the potential energy in the same way that the electric
ﬁeld is related to the electric force. That is, we simply need to multiply the potential by the charge
to get the potential energy. If we choose inﬁnity as our reference point for the potential (
V
∞
= 0),
then the potential of each of the point charges is:
V
=
k
q
r
Furthermore, since the electric force is a conservative force, the change in energy from inﬁnity
to the ﬁnal location does not depend on the path taken. Since we choose
V
∞
= 0,
U
∞
=
q V
∞
= 0
also. Hence, the ﬁnal potential energy of the point charge gives the work done to get it there. The
potential of of charges
q
1
and
q
2
at the location of
Q
is:
V
fin
=
k
h
q
1
2
d
+
q
2
d
i
= 0
The ﬁnal potential energy of charge
Q
is therefore:
U
fin
=
QV
fin
= 0
The total work done in moving the charge in from inﬁnity to its current position is therefore 0.
Problem 24.66
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This note was uploaded on 12/05/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Charge, Energy, Force, Potential Energy

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