Which of the following is correct for equipotential surfaces?
(A) Electric field lines are always perpendicular to equipotential surfaces.
(B) Equipotential surfaces are always spherical in shape.
(C) Work done in moving a charge on equipotential surface is always negative
(D) Two equipotential surfaces never intersect each other
(E) Work done in moving a charge on equipotential surface is always zero
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (D) and (E) only
An equipotential surface is a surface on which the potential has the same value at every point.
(A) Electric field lines are always perpendicular to equipotential surfaces. — Correct. If the field had a component along the surface, a charge would gain or lose energy when moved along it, which contradicts the constant potential.
(B) Equipotential surfaces are always spherical in shape. — Incorrect. They are spheres only for a single point charge; for a uniform field they are planes, and for a dipole they have a different shape.
(C) Work done in moving a charge on equipotential surface is always negative — Incorrect. The work is \( W = q\,(V_2 - V_1) \) and \( V_2 = V_1 \), so it is zero, neither negative nor positive.
(D) Two equipotential surfaces never intersect each other — Correct. At a point where they met, the potential would have two different values and the field would have two different directions.
(E) Work done in moving a charge on equipotential surface is always zero — Correct. This follows from \( W = q\,\Delta V = 0 \).
NCERT (2026-27):
Equipotential Surfaces – “… This is true in general: for any charge configuration, equipotential surface through a point is normal to the electric field at that point. … But this is in contradiction to the definition of an equipotential surface: there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface.”