Problem 3.162

A conductor with resistivity $\rho$ bounds on a dielectric with permittivity $\varepsilon .$ At a certain point $A$ at the conductor's surface the electric displacement equals $D,$ the vector $\mathbf{D}$ being directed away from the conductor and forming an angle $\alpha$ with the normal of the surface. Find the surface density of charges on the conductor at the point $A$ and the current density in the conductor in the vicinity of the same point.