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