Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field, B: ${\textstyle abla \times \mathbf {A} =\mathbf {B} }$. Together with the electric potentialφ, the magnetic vector potential can be used to specify the electric fieldE 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.

Magnetic vector potential was independently introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively to discuss Ampère's circuital law. William Thomson also introduced the modern version of the vector potential in 1847, along with the formula relating it to the magnetic field.