If the field were not normal to the equipotential surface, it would
have non-zero component along the surface To move a unit test charge
against the direction of the component of the field, work would have to
be done But this is in contradiction to the definition of an equipotential
surface: there is no potential difference between any two points on the
surface and no work is required to move a test charge on the surface The electric field must, therefore, be normal to the equipotential surface
at every point