Demagnetizing factors of rectangular prisms and ellipsoids

We evaluate, using exact general formulas, the flux-metric and magnetometric demagnetizing factors, N_f,m, of a rectangular prism of dimensions 2a×2b×2c with susceptibility χ=0 and the demagnetizing factor, N, of an ellipsoid of semiaxes a, b. and c along the c axis. The results as functions of longitudinal and transverse dimension ratios are listed in tables and plotted in figures. The three special cases of b≫(ca)^1/2, b≪(ca)^1/2 , and a=b are analyzed together with the general case, to quantitatively show the validity of approximate formulas for special cases. N_f,m of prisms with any given values of χ may be estimated to an accuracy about 10%, since 1) N_f,m of prisms with a=b are very near those of cylinders, for which the χ dependence has been calculated quite completely; 2) the χ dependence of the transverse N_f,m of prisms with b=∞ (rectangular bars) have recently been calculated completely; and 3) N_f,m(X=∞) for prisms of great longitudinal dimension ratios are close to N of the corresponding ellipsoids. Thus, the existing very incomplete results can be used in some cases satisfactorily, although much work has to be done before the actual χ dependence of N_f,m is available as it is for cylinders