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 ${\displaystyle \mathbf {v} }$, a vector potential is a ${\displaystyle C^{2}}$ vector field ${\displaystyle \mathbf {A} }$ such that $${\displaystyle \mathbf {v} =\nabla \times \mathbf {A} .}$$