Why are electric field lines perpendicular at a point on an equipotential surface of a conductor .
1 answer
the work done on a test charge q moving in an electric field is the force q*E times the distance moved IN THE DIRECTION of the force. The only direction that has NO component of force in the direction of motion is in the direction perpendicular to the force. The force is in the direction of E. Therefore the direction where no work is done so no change in potential energy is perpendicular to E. That is the equipotential.