2.1 Introduction

It is the aim of this chapter to explain how the concept of an excess of the electric current, the charge density, the electric and magnetic fields as well as excesses of the electric displacement field and the magnetic induction may be used to describe the electro-magnetic properties of a boundary layer, or as Gibbs [13] calls it a surface of discontinuity, between two homogeneous phases. Generally speaking there are two aspects of such a boundary layer which must be considered in this context. One is the so-called surface roughness of the interface and the other is the presence of a different material in the boundary layer. The general reason to introduce excess quantities is that for many considerations the detailed structure of the surface is not really needed. If one considers for instance a surface which conducts an electric current, due to a thin layer of metal, it is for many purposes sufficient to know the total current along the surface rather than its precise distribution on length scales comparable to the thickness of the interfacial layer. An extremely important difference between an interface and the bulk of the adjacent phases is the inherent asymmetry of the interface in its response to fields normal to the surface or parallel to the interface. This is eminently clear for a thin metal film between two dielectric media. If one applies an electric field along the film this results in a current while an electric field normal to the film...