Methods of Calculating Forces on Rigid Magnetic Media

Despite 180 years of theory on magnetism, it appears that the practice of calculating forces on magnetic media is ambiguous, as illustrated by a recent article by Casperson. Potentially troubling issues include: Which field B or H should be used? Should the total field be used, or only the external field? And if the latter, what is meant by "external"? Can/should effects of magnetization currents and/or fictitious magnetic poles be included? What is the force on only a portion of a circuit? We review several well-known approaches to magnetic force calculations on elements of rigid circuits, and find it very helpful to use an explicit example to compare and contrast the various methods.