Open AccessOn the mechanical relations of the energy of magnetisation
Author(s) -
G.H. Livens
Publication year - 1916
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1916.0047
Subject(s) - expression (computer science) , sign (mathematics) , basis (linear algebra) , energy (signal processing) , theoretical physics , pure mathematics , field (mathematics) , construct (python library) , mathematics , object (grammar) , physics , computer science , mathematical analysis , quantum mechanics , geometry , artificial intelligence , programming language
1. There still appears to be some uncertainty in the expression for the total energy of a magnetic field, and the mode of its separation into its fundamental constituents, as belonging to the æther and the matter. This is chiefly due to certain discrepancies of sign which exist in the results of the theory in its statical and dynamical aspects. In the statical theory the energy is usually made to appear as though distributed over the field with the densityμ H2 /8π , which corresponds to an æthereal density of amount H2 /8π , but in the dynamical theory the same expressions are obtained with opposite signs. In some quarters it is considered that there are difficulties of a fundamental nature involved in any attempt to remove this discrepancy, and several authors have tried to construct a more consistent theory on a new basis. The object of the present note is mainly to prove that it is possible to interpret the older and more usual form of the theory in a perfectly logical and consistent manner, so that the aforementioned discrepancy does not even present itself. It is shown that the whole difficulty arises partly from an unfortunate choice of æthereal vector, and partly also in the fact that the usual expression for the energy density in the statical case, although in complete agreement with the proper total, is not the proper expression to use in a consistent theory.