Discussion of Maxwell’s Equations

Abstract

The history of electromagnetism, and in particular that part which lead in the 19^th century to the formulation of the equations governing the electromagnetic fields, is studded with the names of the leading scientists of the time. Starting with Gauss, there was a more or less ongoing effort to understand the relationships and to model their interactions, and included efforts by B. Riemann, W. Thompson, M. Faraday, as well as Neumann, Kirchhoff and Weber and Helmholtz. Building on all this work, Maxwell’s great insight was the introduction of the notion of the so-called displacement current, D, a generalization of Faraday’s idea of charge polarization or displacement. Using Faraday’s work and the ideas of elastic continua, Maxwell developed his famous equations, and noting the close agreement between the electric ratio c and the velocity of light, asserted the coincidence of the two phenomena.¹