The depolarization factors for ellipsoids and some of their properties

Abstract

The terminology depolarization factors was firstly highlighted in the study of problems involving magnetic, where, it was initially used to describe magnetic properties of material. Recently, this terminology was investigated to describe composites, improve imaging techniques, and other field of researches related to potential theory in mathematics and physics. Due to our interest in electrical imaging using polarization tensor (PT) and since PT is actually related to the depolarization factors, in this paper, some properties of the depolarization factors are investigated for future applications. The values of these depolarization factors are firstly proven to be non-negative. Based on the previous studies which consider the incomplete elliptic integrals of the first and second kind with some suitable identities, the summation of the depolarization factors are shown to be equal to one. By using these two properties, the value for each depolarization factor for ellipsoid is then explained to be between zero and one. It is also shown in this paper that the depolarization factors can be characterized based on the values of the semi principal axes of the ellipsoid. Reversely, the semi principal axes of the ellipsoid can be classified based on the values of the depolarization factors. All properties presented in this paper could be useful and important in the future especially to use the depolarization factors in any related applications.