Transverse demagnetizing factors of long rectangular bars: I. Analytical expressions for extreme values of susceptibility

The demagnetizing problem should be studied numerically in nonellipsoids with nonzero susceptibility χ, except for a few limiting cases where analytical treatment turns out to be practical. In this work, for an infinitely long bar with rectangular cross section 2a×2b and χ=∞ and −1 in a uniform transverse applied field Ha along dimension a or b, analytical expressions for the surface pole or current distributions and the fluxmetric and magnetometric demagnetizing factors Nf,m are derived using a technique of conformal transformation. From the new as well as the existing formulas, Nf,m(χ=∞,0,−1) are evaluated, plotted, and tabulated as functions of a/b.