Magnetic vector potential

In <a href="/facts/Classical_electromagnetism/vK0YI6dj">classical electromagnetism</a>, magnetic vector potential (often called A) is the <a href="/facts/Vector_quantity/bCLrdksy">vector quantity</a> defined so that its <a href="/facts/Curl_(mathematics)/GuS8dc7o">curl</a> is equal to the <a href="/facts/Magnetic_field/Ta8Ev588">magnetic field</a>: 
 
 
 
 ∇
 ×
 
 A
 
 =
 
 B
 
 
 
 {\textstyle \nabla \times \mathbf {A} =\mathbf {B} }
 
. Together with the <a href="/facts/Electric_potential/Nmqm6hm5">electric potential</a> φ, the magnetic vector potential can be used to specify the <a href="/facts/Electric_field/tt4MooBs">electric field</a> 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 <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, most equations use potentials rather than fields.
Magnetic vector potential was independently introduced by <a href="/facts/Franz_Ernst_Neumann/0F1W6GDG">Franz Ernst Neumann</a> and <a href="/facts/Wilhelm_Eduard_Weber/Wr3s2HPD">Wilhelm Eduard Weber</a> in 1845 and in 1846, respectively to discuss <a href="/facts/Amp%25C3%25A8re%2527s_circuital_law/B6WVCpc6">Ampère's circuital law</a>. <a href="/facts/Lord_Kelvin/LTIxG1jV">William Thomson</a> also introduced the modern version of the vector potential in 1847, along with the formula relating it to the magnetic field.

Magnetic vector potential open-in-new

Magnetic vector potential