Question

If a unit charge is taken from 1 point to another point on an equipotential surface, then the work done is equal to :
(A) Positive
(B) Negative
(C) Zero
(D) Constant

Answer 1

Hint The work done on a unit test charge when moving from 1 point to another is given as work times potential difference. Equipotential surfaces have have zero difference in potential

Complete step by step solution
An equipotential surface is those which have the same potential throughout the entire surface. let us take a unit positive test charge q. if this charge is to be moved from any 1 point with a potential difference ${V_1}$ to some other point with potential difference ${V_2}$ , some work should be done on it. If the work is done against nature, then it would be stored as the potential energy of the body. In our case, we only need to check for moving the body across the equipotential surface.
$W\, = \,qV$
Where q is the mass of charge considered and V is the potential difference between the initial and final points. As the surface is equipotential, it will have the potential everywhere and thus potential difference will be equal to 0. This would further mean that the work done would be 0.

Therefore the correct answer is option C.

Note Work done by electrostatic potential is conservative. This means that it does not depend on the path followed by the unit charge. All that matters is the potential difference between the final and initial points.