Avoidance of contradictions in derivation and in usage of the Maxwell stress tensor in electrical engineering lectures

Abstract

The Maxwell stress tensor has a great significance, for example for the calculation of forces in electromagnetic energy converters, and thus is standard content of advanced lectures during electrical engineering study. However, the derivation and understanding of it is difficult and there is standard literature that is not consistent and thus increases the difficulties. In order to gain a consistent and vivid derivation of the stress tensor for use in electrical engineering lectures, two common variants are analysed from a didactic as well as scientific point of view. It is shown that one variant is consistent whereas the other one can lead to contradictions in case of materials with permeability gradients and thus is not recommended for lectures. Moreover, the resulting tensors of both variants yield different force distributions. For the consistent variant, methods for clarifying the respective force distribution for use in lectures are derived. Finally, a brief consideration on the experimental provability of the results is carried out.