A metallic conducting spherical shell is given a charge. The charge will be uniformly distributed
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → on the outer surface of the shell only
In electrostatic equilibrium the electric field inside the material of a conductor is zero. Take a Gaussian surface lying inside the metal of the shell, just outside the inner surface: the field on it is zero everywhere, so by Gauss’s law it encloses no net charge. With no charge placed in the cavity, the inner surface therefore carries no charge.
The whole charge resides on the outer surface, and because a sphere is perfectly symmetric it spreads there uniformly.
Why the other options are incorrect
Option (1) inside the shell only — Incorrect. No charge can stay inside a conductor (or in its empty cavity); it moves until the field inside the metal is zero.
Option (2) on the inner surface of the shell only — Incorrect. The inner surface would carry charge only if a charge were placed inside the cavity.
Option (4) both on the inner surface and outer surface of the shell — Incorrect. For the same reason, the inner surface carries no charge, so the charge is not shared between the two surfaces.
NCERT (2026-27):
Electrostatic Shielding – “Consider a conductor with a cavity, with no charges inside the cavity. … A related result is that even if the conductor is charged or charges are induced on a neutral conductor by an external field, all charges reside only on the outer surface of a conductor with cavity.”