Problem 3.164

Demonstrate that the law of refraction of direct current lines at the boundary between two conducting media has the form tan $\alpha_{2} / \tan \alpha_{1}=\sigma_{2} / \sigma_{1}$, where $\sigma_{1}$ and $\sigma_{2}$ are the conductivities of the media, $\alpha_{2}$ and $\alpha_{1}$ are the angles between the current lines and the normal of the boundary surface.