Equipotential

In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential.

An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential isosurface), but it can also be a three-dimensional mathematical solid 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 three-dimensional equipotential region.

In the case of a hollow conductor (Faraday cage[4]), the equipotential region includes the space inside.

For the gravity of Earth, the corresponding geopotential isosurface (the equigeopotential) that best fits mean sea level is called the geoid.