A Dynamical Theory of the Electromagnetic Field (Frontier Model Bibliophile Science Source Editions)

Description

In 1865 James Clerk Maxwell gave the electromagnetic field an independent dynamical existence and, from the resulting equations, derived a wave whose speed was that of light. This Frontier Model Bibliophile edition reproduces the paper as it stood in the Royal Society's Philosophical Transactions, with Maxwell's own notation and figures intact, and adds a full apparatus for the modern reader. The 1865 paper stands at the convergence of two traditions that had developed largely apart. On one side lay the Continental electrodynamics of Ampere, Weber, and their successors, framed in terms of forces acting instantaneously at a distance between charges and current elements. On the other lay the experimental electromagnetism of Michael Faraday, who distrusted action at a distance and instead imagined space itself as filled with curved lines of force along which electric and magnetic effects were conveyed. Faraday possessed extraordinary physical intuition but little mathematical formalism; the lines of force were, for him, a picture rather than a calculus. Maxwell's lifelong project was to give that picture a mathematics. His first attempt, "On Faraday's Lines of Force" (1855-56), proceeded by analogy: he treated the lines of force as if they were the streamlines of an incompressible fluid, borrowing the apparatus of hydrodynamics to render Faraday's geometry quantitative. The analogy was illustrative but admittedly artificial. In "On Physical Lines of Force" (1861-62) Maxwell went much further, constructing a detailed mechanical model in which space was filled with molecular vortices whose rotation represented the magnetic field, separated by small "idle wheel" particles whose translation represented electric current. It was within this baroque mechanism that Maxwell was led to a decisive new term. To make the model consistent when the medium was elastic rather than freely conducting, he had to allow that a changing electric state produced a current even in an insulator or in vacuum-the displacement current. In modern notation this is the term that completes Ampere's law, so that H= J+ D/ t. The achievement of the 1865 paper was to retain the displacement current while discarding the vortices and idle wheels. Maxwell now presented the theory as a "dynamical" one in the technical sense of the word: a system whose behaviour follows from general dynamical principles applied to the energy stored in the field, without commitment to any particular mechanism. He set out the relations among the electric and magnetic quantities, the electromotive force, the electric displacement, and what he called the electromagnetic momentum-the vector quantity later named the vector potential-as a connected set. In the paper's own reckoning the theory comprised twenty equations in twenty variables, written out in Cartesian components rather than in the compact vector form familiar today; the four "Maxwell's equations" of the modern textbook are a later condensation, owed chiefly to Heaviside and Hertz. From these relations Maxwell drew the result for which the paper is remembered. Eliminating the field quantities, he obtained equations of wave type, and the speed of the resulting transverse waves was fixed by the ratio of electromagnetic to electrostatic units-a quantity that had been measured by Weber and Kohlrausch. Inserting the experimental value, Maxwell found a propagation speed in close agreement with Fizeau's and Foucault's measurements of the speed of light. He concluded, in a sentence that has become one of the most quoted in physics, that light consists in the transverse undulations of the same medium that is the cause of electric and magnetic phenomena.