Which of the following statements are not true for equipotential surfaces?
A. Equipotential surface through a point is normal to electric field at that point.
B. There is a constant potential difference between any two points on the equipotential surface.
C. No work is required to move a test charge on the equipotential surface.
D. The value of electric potential is constant at all points on the equipotential surface.
E. Equipotential surfaces can not be drawn for an electric dipole.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → B, E only
An equipotential surface is a surface on which the potential has the same value at every point. Because the potential does not change along it, the electric field has no component along it, so the field is normal to it, and moving a charge on it needs no work.
(A) Equipotential surface through a point is normal to electric field at that point — True. The field is perpendicular to the surface at every point.
(B) There is a constant potential difference between any two points on the equipotential surface — Not true. The potential difference between any two points on the surface is zero, not a constant non-zero value.
(C) No work is required to move a test charge on the equipotential surface — True. The work is \( q\,\Delta V = 0 \).
(D) The value of electric potential is constant at all points on the equipotential surface — True. This is the definition of the surface.
(E) Equipotential surfaces can not be drawn for an electric dipole — Not true. Equipotential surfaces can be drawn for any charge distribution, including a dipole.
NCERT (2026-27):
Equipotential Surfaces – “An equipotential surface is a surface with a constant value of potential at all points on the surface. … 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.”