Computation of electromagnetic force densities: Maxwell stress tensor vs. virtual work principle

A couple of fundamental formulae are demonstrated in this paper, which allow a systematic algebraic derivation of local electromagnetic forces in any material, starting from the expression of the energy density of that material. The derivation can be achieved in terms of vector and tensor analysis notions exclusively, provided the distinction is properly made between fields that are ‘flux densities’ (like b) or ‘circulation densities’ (like h). Applying the procedure to the particular case of a nonmagnetic material, the Maxwell stress tensor of empty space and the virtual work principle based formula for nodal forces are both readily found back. This makes the link obvious between those methods. The formulae are further applied to a permanent magnet material.