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A charge q is carried once around a complete circular path in the electrostatic field set up by another fixed point charge Q. The total work done by the electric field on q over one full loop is

1. zero
2. positive
3. negative
4. zero only if Q sits at the centre of the circle, otherwise nonzero

Correct answer: zero

Solution

The electrostatic field is conservative, so the work done by it depends only on the endpoints and equals minus the change in potential energy. Over one complete revolution the charge returns to its starting point, so the potential energy change is zero and the net work is zero regardless of where Q is located.

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