The work done to move a charge along an equipotential from `A` to `B`

Options

A. cannot be defined as `-int_(A)^(B)E.dl`
B. must be defined as `-int_(A)^(B)E.dl`
C. is zero
D. can have a non-zero value

Answer

To solve the problem of finding the work done to move a charge along an equipotential surface from point A to point B, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equipotential Surfaces**:
- An equipotential surface is a surface on which the electric potential is constant. This means that the potential at any point on the surface is the same.

2. **Identifying the Electric Potential**:
- Let \( V_A \) be the electric potential at point A and \( V_B \) be the electric potential at point B. Since both points are on the same equipotential surface, we have:
\[ V_A = V_B \]

3. **Work Done Formula**:
- The work done \( W \) in moving a charge \( Q \) from point A to point B is given by the formula:
\[ W = Q (V_B - V_A) \]

4. **Substituting the Values**:
- Since \( V_A = V_B \), we can substitute this into the work done formula:
\[ W = Q (V_B - V_A) = Q (V_A - V_A) = Q \cdot 0 \]

5. **Conclusion**:
- Therefore, the work done \( W \) to move the charge along the equipotential surface from A to B is:
\[ W = 0 \]

### Final Answer:
The work done to move a charge along an equipotential surface from A to B is **zero**.

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