Difference between revisions of "Wiki:Equipotential surface"
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Latest revision as of 14:40, 18 January 2020
An equipotential region of a scalar potential in threedimensional space is often an equipotential surface, but it can also be a threedimensional region in space. The gradient of the scalar potential (and hence also its opposite, as in the case of a vector field with an associated potential field) is everywhere perpendicular to the equipotential surface, and zero inside a threedimensional equipotential region.
Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the potential difference is zero between the two points. Thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential.
Gravity is perpendicular to the equipotential surfaces of the gravity potential, and in electrostatics and in the case of steady currents the electric field (and hence the electric current, if any) is perpendicular to the equipotential surfaces of the electric potential (voltage).
In gravity, a hollow sphere has a threedimensional equipotential region inside, with no gravity (see shell theorem). In electrostatics a conductor is a threedimensional equipotential region. In the case of a hollow conductor (Faraday cage[4]), the equipotential region includes the space inside.