Demagnetizing factors of rectangular prisms and ellipsoids

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Abstract
We evaluate, using exact general formulas, the flux-metric and magnetometric demagnetizing factors, N/sub f,m/, of a rectangular prism of dimensions 2a/spl times/2b/spl times/2c with susceptibility /spl 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/spl Gt/(ca)/sup 1/2/, b/spl Lt/(ca)/sup 1/2/, and a=b are analyzed together with the general case, to quantitatively show the validity of approximate formulas for special cases. N/sub f,m/ of prisms with any given values of /spl chi/ may be estimated to an accuracy about 10%, since 1) N/sub f,m/ of prisms with a=b are very near those of cylinders, for which the /spl chi/ dependence has been calculated quite completely; 2) the /spl chi/ dependence of the transverse N/sub f,m/ of prisms with b=/spl infin/ (rectangular bars) have recently been calculated completely; and 3) N/sub f,m/(X=/spl infin/) 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 /spl chi/ dependence of N/sub f,m/ is available as it is for cylinders.