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.