Magnetic vector potential, A, is the vector quantity in classical electromagnetism defined so that its curl is equal to the magnetic field:
∇
×
A
=
B
{\textstyle \nabla \times \mathbf {A} =\mathbf {B} \,}
. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.
Vector magnetic potential was first introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively. Lord Kelvin also introduced vector potential in 1847, along with the formula relating it to the magnetic field.