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 $\text{2a×2b}$ and $\mathrm{\chi =\infty }$ and −1 in a uniform transverse applied field $H_a$ along dimension a or b, analytical expressions for the surface pole or current distributions and the fluxmetric and magnetometric demagnetizing factors $N_{\mathrm{f,m}}$ are derived using a technique of conformal transformation. From the new as well as the existing formulas, $N_{\mathrm{f,m}}\text{(χ=∞,0,−1)}$ are evaluated, plotted, and tabulated as functions of $\mathrm{a/b.}$