Force calculation in magnetic field problems using virtual work with only one solution

There are only two common methods for calculating reluctance forces on components in electromagnetic devices. The first, the Maxwell stress method has the advantage that it requires only one solution. However, it is known that it can be inaccurate if the contour is not chosen carefully. The second makes use of virtual work. It suffers from the fact that two, or more, solutions are generally required to yield a differential against distance for the co-energy. This differential yields the force directly. There are obvious advantages if that differential can be obtained directly from one solution. The authors describe such an approach, with supporting evidence from calculations based on the use of a CAD package