Define an equipotential surface.
(N/A) An equipotential surface is a surface with a constant value of electric potential at all points on it.
For any charge distribution,the electric potential $V$ is the same at every point on an equipotential surface.
Consequently,the potential difference between any two points on such a surface is zero $(V_A - V_B = 0)$.
Since the work done in moving a test charge $q_0$ between two points on an equipotential surface is given by $W = q_0(V_A - V_B)$,it follows that no work is done in moving a charge along an equipotential surface.
Furthermore,the electric field lines are always perpendicular to the equipotential surface at every point.
For any charge distribution,the electric potential $V$ is the same at every point on an equipotential surface.
Consequently,the potential difference between any two points on such a surface is zero $(V_A - V_B = 0)$.
Since the work done in moving a test charge $q_0$ between two points on an equipotential surface is given by $W = q_0(V_A - V_B)$,it follows that no work is done in moving a charge along an equipotential surface.
Furthermore,the electric field lines are always perpendicular to the equipotential surface at every point.
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