Fundamental equations of electrom agnetodynamics of fluids: various consequences.

(1) Introduction.-The electromagnetodynamics of fluids combines the dynamics of fluids and electromagnetic theory. It has been independently developed in two theories: magnetohydrodynamics and electrohydrodynamics, depending upon the properties of the fluid considered and the prevalence of either magnetic fields or electric fields. The space permitted here forbids us from going into any appraisal of these theories. The literature on magnetohydrodynamics is vast and a bibliography cannot be given here; for electrohydrodynamics the reader is referred to the studies by G. I. Taylor.' Magnetohydrodynamics gives us the ponderomotive forces produced by externally impressed electric and magnetic fields. However, in general, there are other forces owing to the electromagnetic composition of matter, which magnetohydrodynamics ignores. These are much smaller; nevertheless, they deserve careful consideration. Shockley and James2 recently proposed a "magnetic current force," namely (in meter-kilogram-second-coulomb units): fm = ,E X (B -yioH). However, there is a lapsus calami, for obviously fm is not a force. In this note I shall analyze the problem in its generality, in a continuum theory. Special attention will be paid to the densities of "magnetic current" and "magnetic charge" which seem to play an important role in modern developments. The search3 for magnetic monopoles in ferromagnetic materials and the search proposed by the author4 for ferromagnetic particles in a tornado (whereby one might detect magnetic charges) may disclose new ways for liberation of energy. The subject of this paper may continue to interest the biochemist, as was shown by the good response given to my earlier papers. In an article by Brillouin,5 the biochemist may also find helpful suggestions about other things to look for. (2) Fundamental Equations.-Our first task will be to reformulate the Maxwell stress tensor in order to take into account the electromagnetic properties of matter. Let P (Pi) and M (Mi) be the electric and magnetic polarization vectors: P = D eoE, M = uo-0B H. These are subject to the equations formulated earlier by the writer :'