Chapter 44 - James Clerk Maxwell, A treatise on electricity and magnetism, first edition (1873)

Abstract

Maxwell published about a hundred scientific papers. While his main claim to fame lies in his work on electromagnetism and the kinetic theory of gases, he was interested in almost all branches of physics, both mathematical and experimental, and especially in mechanics, geometry, and optics. Maxwell's researches on electromagnetism were aimed at constructing, at a theoretical level, a unified mathematical theory of electric and magnetic phenomena that would express the methods and ideas of Faraday as an alternative to the theory of Weber. Maxwell presented a combination of two general field equations and implied a new representation of the magnetic effects of closed circuits, according to which the current of conduction in a conducting wire is extended by a current of displacement in the dielectric to form a closed “total current.” He then obtained a wave equation from certain field equations from which he again deduced a speed of propagation equal to ν. He concluded not only that “light and magnetism are affections of the same substance” but also that “light is an electromagnetic disturbance propagated through the field according to the electromagnetic laws.” Thus, Maxwell introduced the notion of electricity as a measurable physical quantity, independent of the hypothesis of electric fluids. He stated Coulomb's law in the same way and defined the key entities of electrostatics. These experiments, soon repeated by many physicists, assured the triumph of Maxwell's theory and its adherents in Britain. They also had the effect of drawing attention to the work of Heaviside.