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
=
Q V
fin
= 0
The total work done in moving the charge in from infinity to its current position is therefore 0.
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 Spring '08
 Any
 Physics, Charge, Energy, Force, Potential Energy, Work, Electric charge, Final Potential Energy

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