Surfacial Electrodynamics. Part Ii. Electromagnetism on A Non-Material Interface in A Deformable Body with Electric and Magnetic Quadrupoles

Abstract

The boundary surface with a thickness of a few Å and bearing electromagnetic surface field densities is modelled as a curved non-material singular surface. This paper, based on the general principles of continuums physics, presents a systematic and rational formulation of a surfacial electrodynamic theory of deformable, electrically polarizable and magnetizable boundary surface in a body, in which the effects of the electric and magnetic quadrupole distributions are included. From the global statement in three dimensions, a global and complete theory of surfacial electrodynamic field equations is derived in two dimensions in agreement with the derived general structure of balance equations of flux on a non-material singular surface in A. Sadiki and K. Hutter [1]. This electrodynamic development is motivated by the classical point-charge model and is restricted to nonrelativistic phenomena (see part I). Various considerations upon the electric and magnetic quadrupole distributions lead to a classification of existing surfacial theories. In particular, when the introduced surfacial fields are ignored, the derived equations reduce to the results of Prechtl [5] and Kafadar [8]. When the electric and magnetic quadrupole distributions are neglected, all surfacial fields appear thanks to the genuine surface dipoles and the derived "Maxwell" equations reduce to the minimal formulation of Albano and Bedeaux [2]. However, when electric and/or magnetic quadrupole distributions (with or without genuine surface dipoles) are considered, then one of the electric and magnetic quadrupole moments contributes to produce surfacial fields and can thus allow, according to [5] and [23], a description of second-order effects on the surface. So, electric and/or magnetic quadrupole moments are important ingredients of a complete formulation of surfacial electromagnetics. When the total surface dipoles are neglected, all surfacial fields disappear and the derived ‘Maxwell’ equations on the surface reduce to the well known classical boundary or jump conditions for space-fields.

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