Question

Why is the direction of the electric field due to a charged conducting sphere at any point perpendicular to its surface?

Answer 1

If the electrostatic field lines are not perpendicular to the surface of the conductor, there will be a tangential component of the electric field. If that is the case, it would create a potential difference and would accelerate the free electrons resulting in current. The only way a conductor can stay at a constant potential throughout or be an equipotential surface, is if the electric field lines are perpendicular to all elemental surfaces of the conductor.

When an additional charge is deposited on the conductor, the free electrons re-arrange themselves in a finite but very short time, until the potential is the same throughout.

Hope it was helpful

Answer 2

Explanation:

The electric field lines are not perpendicular to the surface, there will be a tangential component of the electric field.

This would create a potential difference and would accelerate the free elections resulting in a current.

If the electric field lines are perpendicular to its surface only a conductor can stay at a constant potential throughout or as an equipotential surface.