 Electrical resistivity

Electrical resistivity is the inverse of scalar electrical conductivity in an isotropic Ohmic medium. In its rest frame, $\mathbf{E}={\rho }_{\mathrm{el}}\mathbf{j}$, so the electric field does work per unit volume $\mathbf{j}\cdot \mathbf{E}={\rho }_{\mathrm{el}}|\mathbf{j}{|}^2$. In Gaussian units, finite conductivity gives magnetic diffusivity $\eta =c^2/(4\pi \sigma )$; neglecting this diffusion is a distinct approximation from neglecting electron inertia in Hall magnetohydrodynamics.