Simple force expressions for idealized saturable poles and wedges

Force expressions are presented for simple idealized magnetic pole geometries with (a) infinitely permeable pole material, (b) “square B/H” saturable pole material, and (c) “square M/H” saturable material, the third being the most realistic. The simplicity of the force expressions with saturation is surprising, and important conclusions can be drawn about the role of saturation, the effects of different iron saturation models, and details of the field. For example, for the fundamentally important saturable overlapping rectangular pole configuration, with saturable poles modeled as highly nonlinear, “square M/H” iron, the useful transverse force for positive overlaps is F=μ₀M_sF, twice a comparable value for infinitely permeable poles. This paper is an exploration of how far one can go, using a variety of analytical nonnumerical techniques, in determining fields and forces when saturation effects predominate. The results give useful insights not easily obtained from numerical solutions and provide exact results in certain cases