Question

Why are electric field line perpendicular at a point on an equipotential surface of a conductor
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Answer 1

Answer:

Surface of the conductor is an equipotential surface for static distribution of charge on it. Had it not been so, then charge would flow between points with potential difference. But, then we can not have static charge on the surface.

Now, suppose electric field lines are not perpendicular to the local surface of the conductor . Then electric field will have some component parallel to the surface. This component will give potential difference dV=−E(parallel).dl between the nearby points. Then, the surface is not equipotential surface.