Work done in moving a charge q coulomb on the surface of given charged conductor of potential V is

Options

A. `(V)/(q)` joule
B. Vq joule
C. `(q)/(V)` joule
D. Zero

Answer

To solve the problem of calculating the work done in moving a charge \( q \) coulombs on the surface of a charged conductor with potential \( V \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Electric Potential**:
- The electric potential \( V \) at a point in an electric field is defined as the work done per unit charge in bringing a charge from infinity to that point. For a conductor, the potential is constant throughout its surface.

2. **Identify the Initial and Final Positions**:
- When moving a charge \( q \) on the surface of a charged conductor, we can denote the initial position as \( A \) and the final position as \( B \).

3. **Determine the Potential Difference**:
- The potential difference \( \Delta V \) between two points is given by:
\[ \Delta V = V_{\text{final}} - V_{\text{initial}} \]
- Since the charge is moved on the surface of a conductor, the potential at both points \( A \) and \( B \) is the same, i.e., \( V_{\text{initial}} = V \) and \( V_{\text{final}} = V \).

4. **Calculate the Work Done**:
- The work done \( W \) in moving the charge \( q \) is given by:
\[ W = q \cdot \Delta V \]
- Substituting the potential difference:
\[ W = q \cdot (V - V) = q \cdot 0 = 0 \]

5. **Conclusion**:
- The work done in moving a charge \( q \) coulombs on the surface of a charged conductor of potential \( V \) is \( 0 \).

### Final Answer:
The work done is \( 0 \).

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