Demagnetizing factors of rectangular prisms and ellipsoids

We evaluate, using exact general formulas, the fluxmetric and magnetometric demagnetizing factors, Nf,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. Nf,m of prisms with any given values of χ may be estimated to an accuracy about 10%, since 1) Nf,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 Nf,m of prisms with b = ∞ (rectangular bars) have recently been calculated completely; and 3) Nf,m (χ = ∞) 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 Nf,m is available as it is for cylinders.