📢Electric Susceptibility as a Rank Two Tensor

The analysis demonstrated that the electric susceptibility in an anisotropic medium is a rank two tensor. In such media, the polarization vector and the electric field vector are linearly related by using the summation convention. The proof relies on showing that the electric susceptibility adheres to the mixed-tensor transformation law for a rank two tensor. This was achieved by substituting the known contravariant vector transformation laws for the polarization vector and the electric field vector into the defining constitutive relation and isolating the transformation factor for the electric susceptibility.

Tensor Analysis of Electric Susceptibility in Anisotropic Media | Proof and Derivationviadean on Notion