Potential

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• The mathematical study of potentials is known as potential theory
  Potential theory
  
  In mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions....
  ; it is the study of harmonic function
  Harmonic function
  
  In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice derivative function f : U → R which satisfies Laplace's equation, i.e....
  s on manifold
  Manifold
  
  In mathematics, more specifically topology, a manifold is a topological space in which every point has a neighborhood which "resembles" Euclidean space....
  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 physics
  Physics
  
  Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
  , a potential may refer to the scalar potential
  Scalar potential
  
  A scalar potential is a fundamental concept in vector analysis and physics . Given a vector field F, its scalar potential V is a scalar field whose negative gradient is F,...
   or to the vector potential
  Vector potential
  
  In 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 field
  Field (physics)
  
  In physics, a field is a physical quantity associated to each point of spacetime. A field can be classified as a scalar field, a vector field, or a tensor field, according to whether the value of the field at each point is a scalar , a vector , or, more generally, a tensor, respectively....
   defined in space, from which many important physical properties may be derived.
• Leading examples are the gravitational potential and the electric potential
  Electric potential
  
  At a point in space, the electric potential is the potential energy per unit of electric charge that is associated with a static electric field....
  , 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 potential
  Lennard-Jones potential
  
  A pair of neutral atoms or molecules is subject to two distinct forces in the limit of large separation and small separation: an attractive force at long ranges and a repulsive force at short ranges ....
   and the Yukawa potential
  Yukawa potential
  
  A Yukawa potential is a potential of the formHideki Yukawa showed in the 1930s that such a potential arises from the exchange of a massive scalar field such as the field of the pion whose mass is ....
  .
• In electrochemistry
  Electrochemistry
  
  Electrochemistry is a branch of chemistry that studies chemical reactions which take place in a solution at the interface of an electron Electrical conductor and an ionic conductor , and which involve electron transfer between the electrode and the electrolyte or species in solution....
   there are Galvani potential
  Galvani potential
  
  Galvani potential in electrochemistry, is the electric potential difference between two points in the bulk of two phases. These phases can be two different solids , or a solid and a liquid ....
   and Volta potential
  Volta potential
  
  Volta potential in electrochemistry, is the electric potential difference between two points in the vacuum: close to the surface of metal M1 close to the surface of metal M2; where M1 and M2 are two uncharged metals brought into contact....
  .

See also

• Potential difference
  Potential difference
  
  In physics, the potential difference or p.d. between two points is the difference of the points' scalar potential, equivalent to the line integral of the field strength between the two points....
  
• Potential energy
  Potential energy
  
  Potential energy can be thought of as energy stored within a physical system. It is called potential energy because it has the potential to be converted into other forms of energy, such as kinetic energy, and to do Mechanical work in the process....