The Electromagnetic Wave Equations of James Clerk Maxwell

Abstract

The purpose of this paper is to give an elementary presentation of Maxwell's Wave Equations. It is not the aim of the author to present any new information and the sources of this paper are as follows s The historical-data is taken almost entirely from the book "James Clerk Maxwell and Modern Physics" by Glazebrook except for a few details from "Introduction to Modern Physics" by Richtmyer and Kennard. The field equations, the method of derivation from the differential standpoint and the discussion of the wave equations are entirely from "Principles of Electricity" by Page and Adams, except for the references to Gauss' and Stokes' Theorems. These Theorems, together with the vector derivation are from "Introduction to Theoretical Physics" by Page. Neither of these derivations is the same as that given by Maxwell, but are rather so arranged as to give a good introduction to the subject while involving a minimum of confusion. To facilitate reading the paper is divided into four sections. The first deals with the life of Maxwell and the development of electrical thought prior to the time of Maxwell. The second section deals with the approach of Maxwell to the problem. The third section contains the derivation of the wave equations from the differential form of the field equations and a short discussion of the wave equations. The fourth section contains the derivation of the wave equations by vector means.