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.

Keywords

• eletromagnetismo clássico
• potencial vetor
• história da física
• ensino de física