Question

Why are electric field lines perpendicular at a point on an equipotential surface of a conductor ?
If it were not so, the presence of a component of the field along the surface would violate its equipotential nature.

Detailed Answer :
In an equipotential surface, the potential for a point charge is given by As electric field lines point radially away from the charge, they are perpendicular to equipotential surface. If the electric field lines are not perpendicular to the surface of conductor, there exists a non-zero component of electric field along the surface of conductor where charges could not be at rest.
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