1Properties of equipotential surfaces
1) No point can be at different potentials, so equipotential surface for different potentials can never touch or intersect.
2) Potential energy does not change as a test charge moves over an equipotential surface and hence the electric field can do no work on such a charge. Because of this reason electric field must be perpendicular to the surface at every point so that the force qo will always be perpendicular to the displacement of a charge moving on the surface. Hence, field lines and equipotential surfaces are always mutually perpendicular.
3) Equipotential surfaces are drawn so that there are equal potential differences between adjacent surfaces.
In regions where the magniture of is large, the equipotential surfaces are closer together because the field does a relatively large amount of work on a test charge in a relatively small displacement. In regions where the field is weaker, the equipotential surfaces are farther apart.
4) On a given equipotential surface, the potential V has the same value at every point but in general the electric field does not. For example, at the midpoint of the line joining a dipole, potential is zero but the electric field is not zero.
