A historical analysis of the construction of physical meanings to the concept of vector potential in classical electromagnetism

Abstract

Currently, the concept of vector potential is usually treated in textbooks and taught in university courses of electromagnetism as a mathematical device for the calculation of electric and magnetic fields. However, the historical  investigation  of  the  origin  and  development  of  this  concept, especially in the works of Michael Faraday and James Clerk Maxwell, gave  us  indications  that  these  scientists  attributed  physical   and  mechanical analogical meanings to the quantities that currently receive the  denomination  of  vector  potential.  In  the  contexto  in  which  these scientists worked in the second half of the nineteenth century, the scientific community considered that electromagnetic phenomena occurred in an ether with mechanical properties and that electromagnetic quantities should  have  mechanical  analogues. At the  end  of  this  century,  some physicists, including Oliver Heaviside and Heinrich Hertz reformulated Maxwell's theory, abandoning the physical interpretation given by Maxwell to the vector potential. In this paper, we discuss in a syntactic way  how  this  process  of  change  occurred.  For  this,  we  conducted  a historical study based on primary and secondary sources on the subject and,  finally,  investigated  the  approach  used  in  some  textbooks  of electromagnetism in teaching this concept. We also present indications that the abandonment of physical interpretation of the concept of vector potential  has  been  associated  with  philosophical  and  methodological positions as well as with the interest in solving practical problems in the recent telegraph cable industry in nineteenth-century Britain.