Which of the following is true for a point charge?

The correct answer is Option (2) → The equipotential surfaces are spherical with the charge at the center.

The potential of a point charge, \( V = q/4\pi\varepsilon_0 r \), depends only on the distance r from the charge, so every point on a sphere centred on the charge is at the same potential.

Option (1) The electric potential at a point decreases with the increase in its distance from the charge, if q < 0. — Incorrect. For q < 0 the potential is negative; as r increases it becomes less negative, so it increases towards zero.

Option (2) The equipotential surfaces are spherical with the charge at the center. — Correct. The equipotential surfaces are the surfaces of constant r, i.e. concentric spheres centred on the charge.

Option (3) The electric field intensity varies with the distance inversely. — Incorrect. The field \( E = q/4\pi\varepsilon_0 r^{2} \) follows an inverse-square law, not a simple inverse proportion.

Option (4) The electric field lines are directed radially outward, if q < 0. — Incorrect. Field lines end on negative charge, so for q < 0 they point radially inward, towards the charge.

NCERT (2026-27):
Equipotential Surfaces – “An equipotential surface is a surface with a constant value of potential at all points on the surface. For a single charge \( q \), the potential is given by Eq. (2.8):

    \( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r} \)

This shows that \( V \) is a constant if \( r \) is constant. Thus, equipotential surfaces of a single point charge are concentric spherical surfaces centred at the charge.”