An electron is revolving around a proton. The total work done in one revolution by electric force on the electron will be zero if the trajectory of the electron is

Options

A. circular only
B. elliptical only
C. any closed curve
D. not possible

Answer

To solve the problem, we need to determine the conditions under which the total work done by the electric force on an electron revolving around a proton is zero.

### Step-by-Step Solution:

1. **Understanding Electric Force**:
The electric force between the electron and proton is a central force, which means it acts along the line joining the two charges. This force is responsible for the circular motion of the electron around the proton.

**Hint**: Recall that electric force is always directed towards the center of the circular path when dealing with circular motion.

2. **Conservative Forces**:
The electric force is a conservative force. This means that the work done by this force depends only on the initial and final positions of the electron, not on the path taken.

**Hint**: Remember that conservative forces have the property that the work done around a closed path is zero.

3. **Work Done in One Revolution**:
For a closed path, the work done by a conservative force is zero. Therefore, if the electron completes one full revolution and returns to its starting point, the work done by the electric force during this revolution will be zero.

**Hint**: Think about how work is calculated for a closed loop in terms of potential energy.

4. **Closed Path Requirement**:
Since the work done is zero, it implies that the initial state and the final state of the electron must be the same. This is only possible if the electron travels along a closed path.

**Hint**: Identify what types of paths can be considered closed paths.

5. **Types of Closed Paths**:
The closed path can be circular, elliptical, or any other closed curve. Therefore, the trajectory of the electron can be any closed curve, not just circular or elliptical.

**Hint**: Consider the different geometric shapes that can form a closed loop.

### Conclusion:
The total work done in one revolution by the electric force on the electron will be zero if the trajectory of the electron is any closed curve.

### Final Answer:
The trajectory of the electron must be any closed curve for the total work done by the electric force to be zero.