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.