VII. On the fundamental formulations of electrodynamics

Abstract

1. Modern electrical theory based on Maxwell’s concept of an æthereal displacement current, is generally regarded as being sufficiently complete in itself to cover all actions so far revealed to us, if we exclude those intra-atomic phenomena which probably involve some additional but not necessarily inconsistent action in their working. There, still, however exists a good deal of uncertainty as to the actual results of the development of this theory in certain directions, and no account has yet been taken of the great degree of latitude allowed by it in its simplest and most general form. For example, in most presentations of the theory of energy streaming in the electromagnetic field the discussion is given in a way which might lead one to believe that Poynting’s form of the theory is the only one conceivable. A single alternative has on one occasiont been suggested, but rather as an improvement on Poynting’s form than as an indication of its uncertainty. Whilst it cannot be denied that Poynting’s theory is probably the most appropriate one yet formulated, yet it must be recognised that there are an infinite number of fundamentally different forms each of which is itself perfectly consistent with Maxwell’s theory as expressed in his differential equations of electromagnetic interaction. Again, but now we are on a different plane, it has usually been stated that Maxwell’s theory is not of sufficient generality to cover the cases where there exists the complication of non-linear induction in ferromagnetic media. This view appears to have originated with the idea that the magnetic force is the fundamental æthereal vector of the magnetic field, whereas, as a matter of fact, the only consistent view of the energy relations of such a field leads to the conclusion that the magnetic induction is the true æthereal vector, the magnetic force being an auxiliary vector derived in the process of averaging the minute current whirls into their effective representation as a distribution of magnetic polarity.