Demagnetizing factors of rectangular prisms and ellipsoids

We evaluate, using exact general formulas, the fluxmetric and magnetometric demagnetizing factors, N-f,N-m, of a rectangular prism of dimensions 2a x 2b x 2c with susceptibility chi = 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 much greater than (ca)(1/2), b much less than (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,N-m of prisms with any given values of chi may be estimated to an accuracy about 10%, since 1) N-f,N-m of prisms with a = b are very near those of cylinders, for which the chi dependence has been calculated quite completely; 2) the chi dependence of the transverse N-f,N-m of prisms with b = infinity (rectangular bars) have recently been calculated completely; and 3) N-f,N-m (chi = infinity) 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 chi dependence of N-f,N-m is available as it is for cylinders.