Editing Magnetic vector potential (section)

{{Use American English|date=March 2019}}{{Short description|Integral of the magnetic field}}
{{Electromagnetism|Magnetostatics}}

In [[classical electromagnetism]], '''magnetic vector potential''' (often denoted '''A''') is the [[vector quantity]] defined so that its [[Curl (mathematics)|curl]] is equal to the [[magnetic field]], '''B''': <math display="inline"> \nabla \times \mathbf{A} = \mathbf{B}</math>. 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]]<ref>{{cite journal |last=Neumann |first=Franz Ernst |date=January 1, 1846 |title=Allgemeine Gesetze der induzirten elektrischen Ströme (General laws of induced electrical currents) |url=https://zenodo.org/record/1423608 |journal=Annalen der Physik |volume=143 |issue=11 |pages=31–34 |doi=10.1002/andp.18461430103}}</ref> and [[Wilhelm Eduard Weber]]<ref>W. E. Weber, Elektrodymische Maassbestimungen, uber ein allgemeines Grundgesetz der elektrischen Wirkung, Abhandlungen bei Begrund der Koniglichen Sachsischen Gesellschaft der Wissenschaften (Leipzig, 1846), pp. 211–378 [W. E. Weber, Wilhelm Weber’s Werkes, Vols. 1–6 (Berlin, 1892–1894); Vol. 3, pp. 25–214]. </ref> in 1845 and in 1846, respectively to discuss [[Ampère's circuital law]].<ref>{{Cite journal |last1=Wu |first1=A. C. T. |last2=Yang |first2=Chen Ning |date=2006-06-30 |title=Evolution of the Concept of the Vector Potential in the Description of Fundamental Interactions |url=https://www.worldscientific.com/doi/abs/10.1142/S0217751X06033143 |journal=International Journal of Modern Physics A |language=en |volume=21 |issue=16 |pages=3235–3277 |doi=10.1142/S0217751X06033143 |bibcode=2006IJMPA..21.3235W |issn=0217-751X|url-access=subscription }}</ref>  [[Lord Kelvin|William Thomson]] also introduced the modern version of the vector potential in 1847, along with the formula relating it to the magnetic field.<ref>{{cite journal | last =Yang | first =ChenNing | title =The conceptual origins of Maxwell's equations and gauge theory | journal =Physics Today | volume =67 | issue =11 | pages =45–51 | date =2014 | doi =10.1063/PT.3.2585 | bibcode =2014PhT....67k..45Y }}</ref>