Potential
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In physics, a potential may refer to the scalar potential or to the vector potential. In either case, it is a field defined in space, from which many important physical properties may be derived. Leading examples are the gravitational potential and the electric potential, from which the motion of gravitating or electrically charged bodies may be obtained.
Many entities in physics may be described as vector fields, but it is often easier to work with the corresponding potentials as proxies for the fields themselves. For instance, some force fields exert forces on a body equal to the product of the field and some invariant scalar property of the body, such as the mass or charge. As a body moves through such a force field, it rises and falls in the field's potential, gaining and losing energy through mechanical work. This exchange of energy allows the interaction to be analyzed in terms of simple laws of conservation of energy, without resorting to kinematics, which can be computationally difficult.
The gravitational field is a notable example of such a field. The electric field also behaves this way in many cases, though in the general case it does not (see Electric potential and Faraday's Law).
The mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds. This mathematical formulation arises from the fact that, in physics, the scalar potential is irrotational, and thus has a vanishing Laplacian -- the very definition of a harmonic function.
Specific forces have associated potentials, including the Coulomb potential, the van der Waals potential, the Lennard-Jones potential and the Yukawa potential.
