Distribution of mechanical forces in magnetised material

Although the total force on a piece of iron in a magnetic field is calculable by well known methods, the factors governing its distribution over the iron are less well understood. It is shown that the conceptions of iron as an aggregation of dipoles or of current loops are both inadequate for this purpose, but a combination of the two can be used under certain conditions and leads to the Helmholtz force formula. Maxwell´s formula, based on the dipole concept, is in error. The effect of nonlinearity in the iron characteristic is discussed, and also that of a permeability which varies when the material is deformed. The latter aspect is developed for a particular ideal material, several examples being discussed; it is thereby shown that the variation of permeability with deformation is crucial in determining the distribution of forces.