Magnetic vector potential

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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: ${\textstyle \nabla \times \mathbf {A} =\mathbf {B} }$. 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.

Magnetic vector potential was independently introduced by Franz Ernst Neumann^[1] and Wilhelm Eduard Weber^[2] in 1845 and in 1846, respectively to discuss Ampère's circuital law.^[3] William Thomson also introduced the modern version of the vector potential in 1847, along with the formula relating it to the magnetic field.^[4]