On the description of interfacial electromagnetic properties using singular fields, charge density and currents at a dividing surface

On the basis of the Maxwell equations for the continuously varying electromagnetic fields, describing a system with an interfacial layer between two bulk phases, interfacial electromagnetic fields, charge density and currents are defined at the dividing surface. It is shown that the behaviour of these interfacial electromagnetic field is given in terms of the interfacial charge density and currents as well as the value of the extrapolated bulk fields at the dividing surface. The resulting description is shown to be equivalent to one which uses the Maxwell equations for electromagnetic fields, charge density and currents which are singular at the dividing surface.