An equipotential surface is a surface where every point has the same electric potential.

• Work done $W=q\Delta V$. If $\Delta V=0$ along the surface, $W=0$.
• Since $W=\vec{F}\cdot d\vec{s}=q(\vec{E}\cdot d\vec{s})$, for $W=0$, the electric field $\vec{E}$ must be perpendicular to the displacement $d\vec{s}$ along the surface.
• Thus, $\vec{E}$ is always normal (perpendicular) to equipotential surfaces.