Equipotential

An equipotential is a curve, surface, or region on which a scalar potential has the same value at every point. Moving along it requires no change in potential.

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Scalar field: A function that assigns a scalar value to each point in a space. An equipotential is a level set of a scalar field.
Equipotential surface: A surface on which a scalar potential has one constant value. This is the common three-dimensional form of an equipotential.
Potential theory: The mathematical study of functions governed by Laplace's equation and related equations. It provides the framework for analyzing many physical potential fields.
Electric field line: A curve tangent at every point to the direction of an electric field. Field lines cross electrostatic equipotentials at right angles rather than tracing them.
Gradient: A vector of partial derivatives pointing in the direction of a scalar field's steepest increase. The gradient of the potential is perpendicular to its equipotentials.
Electric potential: Electric potential energy per unit charge at a point in an electric field. Its constant-value surfaces map electrostatic conditions in space.
Laplace's equation: The partial differential equation stating that a function's Laplacian is zero. Electrostatic and gravitational potentials satisfy it in source-free regions.
Nonconservative force: A force whose work can depend on the path taken between two points. A single-valued potential cannot generally describe its work through equipotential differences.
Level set: The set of points where a function takes one specified value. Every equipotential is a level set of its potential.
Gravitational potential: Gravitational potential energy per unit mass at a point in a gravitational field. Its equal-value surfaces describe locations with the same gravitational potential.