On magnetic and electrostatic energy

Abstract

The present paper is preliminary to another dealing with the thermodynamics of magnetization. The treatment of magnetic energy in most of the standard text-books is unsatisfactory, because the relations deducible directly from Maxwell's equations are inextricably mixed up with the assumption that the ratio of the magnetic induction B to the magnetic field intensity H is a constant. In order to extend the dynamical treatment of magnetic energy to a thermodynamic treatment which takes account of temperature and pressure variations it is essential not to assume that the ratio B/H is a constant. For even supposing that B/H may be assumed constant in the electrodynamic treatment, this merely means that its value is independent of B and H, but it will usually not be independent of temperature and pressure. Suppose, for instance, that for isothermal variation the ratio B/H remains constant, then for adiabatic variations it will usually not remain constant. Similarly if B/H is constant at constant pressure, it will not be constant at constant volume. In order to deduce the accurate thermodynamic relations, it is therefore essential to be clear about the eletrodynamic formulae for magnetic energy for the general case that B is any single valued continuous function of H. Such formulae will be applicable not only to diamagnetic and paramagnetic substances but also to ferromagnetic substances and even permanent magnets provided we exclude hysteresis. The treatment presented here is an elaboration of that of Cohn. Some of the errors made by other authors are discussed in a later section. 2—Notation Our notation agrees, so far as possible, with that of the S. U. N. Committee and with that of Cohn. In particular we leave open the question whether ε 0 and μ 0 are identically equal to unity. The most important symbols used are the following:—