Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 6 / d / Solution

An axial electric field produces $\mathbf{J}=d\mathbf{E}$, so the observation sets $d=0$ and imposes no restriction on the transverse or antisymmetric parts. ThusA symmetric conductivity tensor would further require $h=0$, but axial rotational invariance alone does not require this.