Physics · Ch 1 — Electrostatics
Equi-potential Surface
Equi-potential Surface
A surface on which the electric potential has the same value at every point is called an equipotential surface. For an isolated point charge, the equipotential surfaces are a family of concentric spheres centred on the charge, since V = kq/r depends only on the distance r; for a uniform electric field, the equipotential surfaces are a family of flat parallel planes perpendicular to the field direction. Two important general properties follow. First, since the potential is the same everywhere on an equipotential surface, moving a charge from one point to another point on the same equipotential surface requires exactly zero net work -- the electric potential difference (and hence the work per unit charge) is zero along any path confined to a single equipotential surface. Second, the electric field is always perpendicular to the equipotential surface passing through any given point: if the field had any component along the surface, that component would do work moving a charge along the surface, contradicting the fact that the potential (and hence the work) is constant on that surface; consequently field …
What this figure shows. A set of concentric spherical surfaces, drawn as circles of increasing radius around a single point charge, are shown with the field lines (straight radial arrows) crossing every one of the spheres at a perfect right angle. Each sphere is labelled with its own constant potential value, decreasing as radius increases, illustrating that for an isolated point charge the equipotential surfaces are exactly concentric spheres centred on the charge, and that the radial field lines are everywhere perpendicular to them, …
What this figure shows. A more complicated family of curved (non-spherical) equipotential surfaces is drawn around a pair of charges, closer together and more distorted near each individual charge, and merging into large, nearly-spherical surfaces far from the pair where the two charges together look almost like a single point charge (or, for an exact dipole, flattening into the zero-potential equatorial plane exactly midway between them). The field lines, wherever drawn, still cross every one of these equipotential surfaces perpendicularly, confirming that the perpendicularity rule holds for any charge configuration, h …