Potential

Encyclopedia

- In linguistics, the potential mood
- The mathematical study of potentials is known as potential theoryPotential theoryIn mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...

; it is the study of harmonic functionHarmonic functionIn mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R which satisfies Laplace's equation, i.e....

s on manifoldManifoldIn mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....

s. 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. - In physicsPhysicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a potential may refer to the scalar potentialScalar potentialA scalar potential is a fundamental concept in vector analysis and physics . The scalar potential is an example of a scalar field...

or to the vector potentialVector potentialIn vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field....

. In either case, it is a fieldField (physics)In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...

defined in space, from which many important physical properties may be derived.- Leading examples are the gravitational potential and the electric potentialElectric potentialIn classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...

, from which the motion of gravitating or electrically charged bodies may be obtained. - Specific forces have associated potentials, including the Coulomb potential, the van der Waals potential, the Lennard-Jones potentialLennard-Jones potentialThe Lennard-Jones potential is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. A form of the potential was first proposed in 1924 by John Lennard-Jones...

and the Yukawa potential. - In electrochemistryElectrochemistryElectrochemistry is a branch of chemistry that studies chemical reactions which take place in a solution at the interface of an electron conductor and an ionic conductor , and which involve electron transfer between the electrode and the electrolyte or species in solution.If a chemical reaction is...

there are Galvani potentialGalvani potentialGalvani potential in electrochemistry, is the electric potential difference between two points in the bulk of two phases...

and Volta potentialVolta potentialVolta potential in electrochemistry, is the electric potential difference between two points in the vacuum:...

. - In ThermodynamicsThermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

potential refers to thermodynamic potential.

- Leading examples are the gravitational potential and the electric potential