Question

why must electrostatuc field be normal to the surface at every point of charged condouctor

Answer 1

If the electrostatic field lines are not perpendicular to the surface, there will be a component of the electric field which is tangential to the surface of the conductor. 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.


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