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THE USE OF THE DISPLACEMENT VECTOR IN ELECTRO-MAGNETIC THEORY
STANFORD UNIV CALIF MICROWAVE LAB
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Problems in the electrodynamics of charged fluids often require calculation of the charge and current densities, given prior knowledge of the initial distributions and the displacement vector field. In this paper, solutions are obtained for these new distributions, with the property that if the initial distributions have a sharply defined boundary, terms arise which can be interpreted as distributions of electric charge and current multipoles located on the initial boundary surface. These solutions can not be considered valid near the initial boundary, but prove to be useful in that many of their properties are given correctly. The electromagnetic potentials due to the charge and current densities in the displaced configuration are calculated, and form the basis for a discussion of the complicated boundary value problem encountered in the description of the electrodynamics near the boundary surface. The results are directly applicable to the theory of high frequency electron tubes, and certain formulae are of use in hydrodynamics and elasticity. Author
APPROVED FOR PUBLIC RELEASE