Question

If the electric field \[\vec{E}\] had a component along (tangent to) an equipotential surface, what contradiction would arise?

Options

• Two equipotential surfaces would be forced to intersect

• The potential difference between two points on the surface would become infinite

• The charge would lose mass while moving along the surface

• It would exert a force on a charge along the surface, doing non-zero work — contradicting the zero-work requirement

Answer 1

If \[\vec{E}\] had a component along the surface, it would exert a force on a charge along the surface, doing non-zero work — contradicting the fact that no work is done in moving a charge along an equipotential surface. Hence, the tangential component must be zero, forcing \[\vec{E}\] to be perpendicular to the surface.