Maxwell's stress tensor and the forces in magnetic liquids

Abstract

Maxwell's stress tensor is well known from electromagnetic theory. But correct application of it to practical problems is by no means general knowledge even among experts. In this article we present a survey of the electromagnetic stress tensor and of the electromagnetic forces in strongly polarizable materials. We relate the observed ponderomotoric phenomena to the stress tensor and we present a number of applications in modern devices and processes using ferromagnetic colloids, so-called ferrofluids. We emphazise the correct applications of the stress tensor to these examples in contrast to common popular usage of a so-called “electromagnetic pressure”. We predict some new effects, e.g. density variations and pressure measurements in ferrofluids. Our work is based on two preceding articles by the present authors [4, 33] wherein the electromagnetic stress tensor is deduced from conservation laws together with Maxwell's equations and with thermodynamic relations.