By George J. Spix

Introduction

James C. Maxwell (1831-1879) published his Electromagnetic Field Equations in 1864. He brought together previous experimental work and concepts of Gauss, Ampere and Faraday and his own knowledge of mathematics to present his analysis of electromagnetic fields. With his field equations, Maxwell calculated the speed of electromagnetic propagation. The result showed that the speed of propagation was equal to the speed of light, which indicated that light is also an electromagnetic field. Maxwell predicted the discovery of the radio waves that Hertz found in 1888.

Maxwell’s equations are the bases for the theory of electromagnetic fields and waves. They are used in the design of antennas, transmission lines, cavity resonators, fiber optics and solving radiation problems.

This tutorial paper derives Maxwell’s equations using the methods followed by college texts, and as such must start with the laws and experiments of Gauss, Ampere and Faraday. In the format followed by the paper, one of Maxwell’s equations, in integral and differential form will be stated at the beginning of each section followed by its derivation. Finally, three examples will be given in the use of the equations. We will find the velocity of electromagnetic radiation, the characteristic impedance of free space and the analytic reason for using sine waves to describe electromagnetic waves. The calculus required for the derivations and problems is presented in detail to remove the difficulties of the mathematics from being an impediment to the students in making the equations their own.

This paper is the author’s rewritten college notebooks and all of it can be garnered from college textbooks.