A magnetic vector potential corresponding to a centrally conservative current element force

Abstract

The magnetic vector potential (Coulomb gauge) is commonly introduced in magnetostatic chapters of electromagnetism textbooks. However, what is not typically presented are the infinite subsets of the Coulomb gauge associated with differential current elements. This work provides a comparison of various differential magnetic vector potentials, differential magnetostatic potential energies, as well as differential current element forces as a collective work not available elsewhere. The differential magnetic vector potential highlighted in this work is the Coulomb-Ampère gauge corresponding to the centrally conservative Ampère current element force. The centrally conservative force is modeled as a mean valued continual exchange of energy carrier mediators accounting for both the differential magnetostatic potential energy and Ampère current element force of two differential current elements.