# Equipotential lines and equipotential surfaces

As its name suggest a line of equipotential is a line joining points of equal potential just like a contour line on a mountainside. Since E = -dV/dx the closer the lines of equipotential are the greater is the field strength.

An equipotential surface is a surface which joins points of equal potential and therefore a surface on which the potential does not vary. This means that if you connected a wire between two points on the surface no current would flow between them. The analogy with gravity could be two small lakes at equal height on a mountain side - if a pipe connected the two together no water would flow along it in either direction.

Looking at it in another way on the surface of a conducting solid electric currents are free to flow - they would do this until the potential at all points is the same and so the surface of the solid would become an equipotential surface.

A line of force is always at right angles to an equipotential surface it shows the "downhill" motion of a positive charge.

## Equipotentials for a radial field

The diagrams for some other arrangements of charge are shown in the file: Equipotentials and fields