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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. + 18 V A line of force is always at right angles to an equipotential surface it shows the "downhill" motion of a positive charge. Equipotentials for uniform fields + 18 V 18 V 16 V 14 V 12 V 10 V 8V Potential E = -dV/dx is constant. 6V 4V 2V 0V Distance from top plate 1 Equipotentials for a radial field Potential Potent (V) ial (V) Distance Electric field lines 20 V 10 V 15 V Lines of equal potential The diagrams for some other arrangements of charge are shown in the file: 16-19/Electricity and magnetism/Electrostatics/Text/Equipotentials and fields 2