Question

If charge \(+q\) is taken from one point to another over an equipotential surface, then

• A. work done on the charge continuously increases.
• B. work is done by the charge.
• C. work done on the charge is constant.
• D. no work is done.

Hint:

Work done equals charge times potential difference, which is zero on an equipotential surface.

Answer 1

The Correct Option is D

Step 1: Approach
Use the force direction.

Step 2: Geometry
The electric field is perpendicular to an equipotential surface. A displacement along the surface is perpendicular to the field, so $\vec F\cdot d\vec s=qE\,ds\cos90^\circ=0$.

Step 3: Answer
No work is done, option (D).

Final Answer:
The potential difference is zero on an equipotential surface, so no work is done, option (D). \[ \boxed{\text{No work is done}} \]