The Collaborative International Dictionary
Equipotential \E`qui*po*ten"tial\, a. [Equi- + potential.] (Mech. & Physics) Having the same potential.
Equipotential surface, a surface for which the potential is for all points of the surface constant. Level surfaces on the earth are equipotential.
Wiktionary
a. Having equal potential. alt. Having equal potential. n. A region whose every point has the same potential.
Wikipedia
Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in n-dimensional space is typically an (n−1)dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field.
Note that an equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface, but it can also be a three-dimensional 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 three-dimensional 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 three-dimensional equipotential region inside, with no gravity (see shell theorem). In electrostatics a conductor is a three-dimensional equipotential region. In the case of a hollow conductor ( Faraday cage), the equipotential region includes the space inside.
A ball will not be accelerated by the force of gravity if it is resting on a flat, horizontal surface, because it is an equipotential surface.
Usage examples of "equipotential".
In the language of physics, the stratus forms an equipotential surface in the gravitational field permeating the earth's atmosphere.
The geoid is the equipotential surface of the earth's gravitational field that approximates the mean sea surface.
And since, as with any conservative vector field (one in which energy potentials can be defined), any point of a gravity field is described by a line of force and the equipotential passing through it, the field coordinate system can serve as a local standard of rest.