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":

... 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 ...

... 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 ...

... 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 ...

... 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)