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A configuration of point charges has potential energy U1. A charge q is brought into the configuration without moving any of the existing charges, raising the potential energy to U2. The electric potential at the location where q is placed (due to the original charges) is:

1. (U2 - U1) / q
2. (U1 - U2) / q
3. (U1 + U2) / (2q)
4. (U2 - U1) / (2q)

Correct answer: (U2 - U1) / q

Solution

Adding charge q to a point of potential V increases the system energy by q*V. Hence V = (U2 - U1)/q.

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