The Conductivity and the Depolarization Factor of a Spheroid based on its Polarization Tensor and Volume

The polarization tensor can be used to describe an object presented in an electric field. This is useful in getting accurate image about the object with electrical imaging device or increasing the likelihood of detecting the object with metal detector. Given the first order polarization tensor and the volume of a spheroid, some properties of the spheroid, such as its conductivity and depolarization factor, have not yet been investigated. Thus, this study aims to propose a method to determine the conductivity and depolarization factor of the spheroid, based on its first order polarization tensor and volume. In order to achieve this, the system of nonlinear equations is first derived based on the given first order polarization tensor, before being solved by the Newton's method. Numerical examples are then provided to demonstrate and justify the proposed algorithm. The findings show that the error for the computed conductivity and depolarization factor is small, suggesting that the proposed algorithm is reliable. In addition, the relationship between the spheroid's volume and conductivity is also discussed. The results illustrate an inverse relationship between the conductivity and depolarization factor when considering a positive definite first order polarization tensor. In contrast, for a negative definite first order polarization tensor, the findings reveal a positive correlation between spheroid's conductivity and its volume. The results obtained can then be used to characterize the spheroid based on its first order polarization tensor and also its volume. This provides additional information about the spheroid, which may contribute to the improvement of future techniques in electrical imaging and metal detection.