A point charge q is rotating along a circle in the electric field generated by another point charge Q. The work done by the electric field on the rotating charge in one complete revolution is :

Question

Accepted Answer

The correct answer to the question is Option 3: zero. Let's delve into the reasoning behind this and explain why the other options are incorrect.

### Explanation for Option 3: Zero

When a point charge $ q $ rotates along a circle in the electric field generated by another point charge $ Q $, the work done by the electric field on the rotating charge in one complete revolution is zero. This is because the electric field is a conservative field. In a conservative field, the work done on a charge moving along a closed path is zero.

In this scenario, the charge $ q $ completes a full circle, which is a closed path. Since the electric field is conservative, the net work done over one complete revolution is zero. This is analogous to gravitational fields, where the work done by gravity on an object moving in a closed path is also zero.

### Explanation for Why Other Options are Incorrect

1. **Option 1: Ever positive**
   - If the work done were ever positive, it would imply that the charge $ q $ gains energy from the electric field in one complete revolution. However, in a conservative field, the net work done over a closed path is zero, not positive. Therefore, this option is incorrect.

2. **Option 2: Ever negative**
   - If the work done were ever negative, it would mean that the charge $ q $ loses energy to the electric field in one complete revolution. Again, due to the conservative nature of the electric field, the net work done over a closed path is zero, not negative. Thus, this option is incorrect.

3. **Option 4: May be positive or negative**
   - This option suggests variability in the work done, which contradicts the fundamental property of conservative fields. In a conservative field, the work done over a closed path is always zero, not variable. Hence, this option is incorrect.

In conclusion, the work done by the electric field on the rotating charge in one complete revolution is zero, as explained by the properties of conservative fields. This supports Option 3 as the correct answer.