Question

Which of the following statements related to an equipotential surface is/are CORRECT?

• A. Work is done on moving a test particle on an equipotential surface
• B. Only one equipotential surface can exist at any point in space
• C. The potential is constant on an equipotential surface
• D. Field lines at any point are always parallel to their equipotential surface

Hint:

Equipotential surfaces are always perpendicular to electric field lines, and no work is done while moving a test charge along them.

Answer 1

The Correct Option is B, C

Step 1: Check Option (A).
On an equipotential surface, the potential is constant. Therefore, no work is required to move a test charge on the surface, since work done is \[ W = q \, \Delta V = 0 \] Hence, Option (A) is incorrect. Step 2: Check Option (B).
At a given point in space, the potential has a unique value. Since an equipotential surface is defined as the locus of all points having the same potential, only one equipotential surface can pass through a given point.
Thus, Option (B) is correct. Step 3: Check Option (C).
By definition, an equipotential surface is one where the potential remains constant everywhere.
Thus, Option (C) is correct. Step 4: Check Option (D).
Electric field lines are always perpendicular, not parallel, to equipotential surfaces. This ensures no work is done in moving a charge along the surface.
Thus, Option (D) is incorrect. Step 5: Conclusion.
The correct statements are (B) and (C). \[ \boxed{\text{Correct Answer: (B) and (C)}} \]