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. circulary only
B. elliptical only
C. any closed curve
D. not posssible

Answer

To solve the question, we need to determine the type of trajectory that results in zero work done by the electric force on the electron as it revolves around the proton.

### Step-by-Step Solution:

1. **Understanding the Forces Involved**:
The electron is negatively charged and the proton is positively charged. The force between them is the electrostatic force, which is attractive and acts along the line connecting the two charges.

**Hint**: Recall that the electrostatic force is described by Coulomb's law.

2. **Identifying the Nature of the Force**:
The electrostatic 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 by Conservative Forces**:
For a conservative force, the work done (W) can be expressed as:
\[ W = W_{\text{final}} - W_{\text{initial}} \]
If the electron returns to its initial position after one complete revolution, the work done will be zero:
\[ W = 0 \implies W_{\text{final}} = W_{\text{initial}} \]

**Hint**: Think about what it means for the initial and final states to be the same.

4. **Closed Path Requirement**:
The condition for the work done to be zero indicates that the trajectory of the electron must be a closed path. This means that after one complete revolution, the electron ends up at the same position where it started.

**Hint**: Consider different shapes that can be closed paths.

5. **Types of Closed Paths**:
The simplest closed path is a circle. However, other shapes like ellipses or any closed curve will also satisfy this condition. Therefore, the trajectory of the electron can be circular, elliptical, or any other closed curve.

**Hint**: Visualize different closed shapes and remember that all must return to the starting point.

6. **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 a closed curve.