Question

A negatively charged particle revolves in a clockwise direction around a positively charged sphere. The work done on the negatively charged particle by the electric field of the sphere is:

a. zero
b. negative
c. positive

Answer 1

\[W=\int_C\overrightarrow{F}\cdot\overrightarrow{v}dt\]from the image (assuming it is a circle) you can see that the force is always at a right angle to the direction of motion of the charge. Also note that the charge will eventually return to its original position, whether the orbit is a circle or an ellipse.
Both these ideas lead to the same answer: zero.

Answer 2

*actually v in the figure above should be pointed down (clockwise motion), but you get the same answer.