Generalization of Maxwell Stress Tensor Method for Magnetically Anisotropic Regions

This article comments on the Maxwell stress tensor method for force calculation in magnetically anisotropic regions. Force acting on the magnetically isotropic region can be always represented by means of Maxwell stress tensor surface integral. However, the magnetic anisotropy causes the asymmetry of Maxwell stress tensor. Subsequently, the force cannot be always evaluated by the surface integral of the Maxwell stress tensor, only. This article points out that the surface integral has to be often supplemented by the volume integral of a defined residual vector. The residual vector does not vanish in the case of anisotropy and has to be incorporated into the Maxwell stress tensor method. Appropriate examples of force evaluations for anisotropic ball levitating in the electromagnetic field are presented. The total force value is four times checked by Maxwell stress tensor modified method (for cylindrical and spherical coordinate systems), sum of physical components (Lorentz and material forces), and coenergy method, subsequently.