Identify the correct properties of equipotential surfaces among the following.
(A) No work is done in moving a test charge over an equipotential surface.
(B) Electric field is always normal to the equipotential surface at every point.
(C) Equipotential surfaces are closer together in the regions of the strong electric field and farther apart in the regions of the weak electric field.
(D) No two equipotential surfaces can intersect each other.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D)
An equipotential surface is a surface on which the potential has the same value at every point.
(A) No work is done in moving a test charge over an equipotential surface. — Correct. The work done is \( W = q\,\Delta V \), and \( \Delta V = 0 \) between any two points of the surface.
(B) Electric field is always normal to the equipotential surface at every point. — Correct. A field component along the surface would mean work is done along it, contradicting (A); so the field is normal to the surface.
(C) Equipotential surfaces are closer together in the regions of the strong electric field and farther apart in the regions of the weak electric field. — Correct. For the same step \( \Delta V \), \( \Delta r = \Delta V/E \): a strong field means a small spacing.
(D) No two equipotential surfaces can intersect each other. — Correct. At a point of intersection the field would have two different normal directions, which is impossible because the field at a point has a single direction.
NCERT (2026-27):
Equipotential Surfaces – “… If the field were not normal to the equipotential surface, it would have non-zero component along the surface. To move a unit test charge against the direction of the component of the field, work would have to be done. 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. The electric field must, therefore, be normal to the equipotential surface at every point.”