Why is the electric field at the outer surface of a hollow charged conductor is normal to the surface?
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Why must electrostatic field be normal to the surface at every point of a charged conductors?
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.
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