Equipotential Surfaces

An equipotential surface is a surface with a constant value of potential at all points on the surface. For a single charge q, the potential is given by

This shows that V is a constant if r is constant. Thus, equipotential surfaces of a single point charge are concentric spherical surfaces centre at the charge.

No work in done in moving from one point to another in equipotential surface.

For a uniform electric field E, say, along the x -axis, the equipotential surfaces are planes normal to the x -axis, i.e., planes parallel to the y-z plane. Equipotential surfaces for (a) a dipole and (b) two identical positive charges are shown in Fig.