The effect of material stresses on electromagnetic boundary conditions

The appearance of a layer of charge or current on the boundary of a material usually implies that a discontinuity in an electromagnetic field occurs at that boundary. The converse is not necessarily true. The reaction of the electromagnetic field to the charge or current layer is a stress communicated across the boundary. Determination of the charge or current on a boundary must take all the stresses and electromechanical interactions at the boundary into account. Calculating surface currents or charges derived from electromagnetic field quantities alone, ignoring mechanical stresses, may lead to wrong answers at material boundaries. In short, the occurrence of charge or current on material in the presence of an electromagnetic field is intimately related to momentum conservation. A postulate equivalent to identifying the Poynting vector with energy flow is introduced, linking surface currents and charges to momentum balance at the surface. A formally correct method for calculating surface currents and charges based on momentum balance is described.