The unique eccentricity of a prolate spheroid based on its depolarization factor

• Main Authors: Ahmad, Syafina, Yunos, Nurhazirah Mohamad, Khairuddin, Taufiq Khairi Ahmad, Embong, Ahmad Fadillah
• Format: Conference Proceeding
• Language: English
• Subjects: Depolarization; Eccentricity; Image reconstruction; Magnetic properties; Mathematical analysis; Nonlinear equations; Oblate spheroids; Physical properties; Prolate spheroids; Tensors; Uniqueness
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0192113

The concept of the depolarization factors has been extensively practiced in many studies such as when dealing with magnetic field that is related to the physical properties of an object. In the image reformation, these depolarization factors are often associated with the first order Polarization Tensor (PT) that characterizes and describes some conducting objects with varying conductivity contrasts in order to attain a better image reconstruction of the objects. In this paper, we review some mathematical properties of the depolarization factors for spheroid, also known as an ellipsoid consists of two circumferential semi axes, as well as the mathematical formulation to determine the depolarization factor for prolate and oblate spheroid. In order to obtain the eccentricity by depolarization factors in both prolate and oblate spheroids, it can be calculated and solved by using any suitable numerical computations to find the solution for nonlinear equation. In our research regarding the depolarization factors, we often used Newton’s method to determine the eccentricity. However, in this study, we want to investigate the uniqueness of the eccentricity from a given depolarization factor specifically for a prolate spheroid. By using the explicit formula of depolarization factor for prolate spheroid, we investigate some properties of its depolarization factor for further analysis. We have shown that the depolarization factor for prolate spheroid is a decreasing function (negative function) by investigating its derivative. After that, the value for the depolarization factor of prolate spheroid is then determined to be between 0 and 13. Consequently, by utilizing these two properties, the function is one-to-one which implies the existence of a unique solution eccentricity that corresponds to the values of the semi principal axes of the spheroid.