Surface-integral methods of calculating forces on magnetized iron parts

The force exerted on an iron part in a magnetic field may be calculated by a number of different methods, all of which give equivalent force distributions confined principally to a surface. Seven different methods, giving rise to five different surface force intensities, are shown to result in the same total force. Additional volume force components are obtained and a new expression for the actual distribution of force, consistent with all of the methods of calculation, is derived. A common interpretation of the well-known Maxwell field stresses in iron is shown to be incorrect. When the field is specified numerically the calculation of force in terms of surface integrals has certain advantages over the virtual-work method, and it is shown that simple analytic expressions for force which are usually obtained in this way may be easily derived as surface integrals. Practical applications are considered.