A unique distribution of forces in permanent magnets using scalar and vector potential formulations

By the virtual work method, the electromagnetic force distribution can be calculated either by using the energy or the co-energy. In a rigid permanent magnet, the obtained force densities are extremely dependent on the expressions used to define the energy and the co-energy. It is demonstrated that the use of the appropriate expressions provides the same local force distribution using scalar (co-energy) or vector potential (energy) formulations.