# 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 gradient is a given vector field.

Formally, given a vector field v, a vector potential is a vector field A such that

If a vector field v admits a vector potential A, then from the equality

(divergence of the curl is zero) one obtains

which implies that v must be a solenoidal vector field.

Read more about Vector Potential:  Theorem, Nonuniqueness

### Other articles related to "vector potential, potential, vector, vector potentials, potentials":

Examples - Abelian Higgs Mechanism
... But the zero value of the vector potential is not a gauge invariant idea ... The vector potential changes the phase of the quanta produced by the field when they move from point to point ... The second term is the extra potential energy when the field varies from point to point ...
Solenoidal Vector Field - Properties
... The fundamental theorem of vector calculus states that any vector field can be expressed as the sum of an irrotational and a solenoidal field ... The condition of zero divergence is satisfied whenever a vector field v has only a vector potential component, because the definition of the vector potential A as automatically results in the ...
Einstein's Hole Argument
... They do not determine the vector potential though, because the vector potential depends on an arbitrary choice of gauge ... transformation are physically equivalent, just as two different vector potentials which differ by a gauge transformation are equivalent ... transformation which will only affect the vector potential tomorrow ...
Vector Potential - Nonuniqueness
... The vector potential admitted by a solenoidal field is not unique ... If A is a vector potential for v, then so is where m is any continuously differentiable scalar function ...
Gauge Fixing - Coulomb Gauge
... for "semi-classical" calculations in quantum mechanics, in which the vector potential is quantized but the Coulomb interaction is not ... The Coulomb gauge has a number of properties The potentials can be expressed in terms of instantaneous values of the fields and densities (in SI units) where ρ(r, t) is the electric charge density ... The instantaneous nature of these potentials appears, at first sight, to violate causality, since motions of electric charge or magnetic field appear everywhere instantaneously as changes to the potentials ...

### Famous quotes containing the word potential:

Most days I feel like an acrobat high above a crowd out of which my own parents, my in-laws, potential employers, phantoms of “other women who do it” and a thousand faceless eyes stare up.
—Anonymous Mother. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 2 (1978)