Scalar potential

A scalar potential is, mathematically, a scalar field whose negative gradient is a given vector field. If the scalar potential is denoted by the Greek letter φ and the vector field it generates as v, then

Related Topics:
Scalar field - Gradient - Vector field

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: mathbf{v} = - abla phi qquad qquad (1) .

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The vector field can be a velocity field or a force field. Equation (1) therefore means a movement or acceleration towards the direction in which there will be a decrease of potential.

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Physically, the scalar potential is similar or identical to potential energy. Any conservative force field can be represented as the negative gradient of some scalar potential.

Related Topics:
Potential energy - Conservative force

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Any lamellar field can be represented as having a scalar potential, but a solenoidal field generally does not have a scalar potential (except the degenerate case when it is Laplacian).

Related Topics:
Lamellar field - Solenoidal field - Laplacian

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