Magnetostatic Stress: Insightful Analysis and Manipulation of Maxwell's Stress Equation for Magnetostatics

Maxwell's stress equation for magnetostatics identifies a tensile stress in the direction of the magnetic field and a pressure normal to this direction. For an isolated, differential current element, Maxwell's stress equation is recast using a variant of Stokes' Theorem. The recast stress equation eliminates the tensile stress in the direction of the magnetic field and establishes a stress that is normal to the magnetic field, directed inward toward the differential current element. For two separated current elements, Maxwell's stress equation is also recast, identifying a constant line stress directionally aligned between the two current elements. The magnitude of the line stress is equivalent to the two current element Neumann force. The analysis and manipulation of Maxwell's stress equation provides some insight into magnetostatic stresses and establishes additional tools for the electrical engineer when analyzing magnetostatic system stresses.