An interface between a dielectric and a medium containing charge carriers with moderate mobility is considered. In equilibrium, stochastic fluxes of positive and negative particles toward the surface have equal average current density j0, and we suppose that the surface absorbs all falling charges. All over the surface, this results in the emergence of oppositely charged spots of various sizes D fluctuating and interacting with each other. Fourier expansion reduces this collection of interacting spots to the ensemble of independently fluctuating charge density waves. An exact solution of the Poisson equation for a single wave on a flat surface was obtained and provided strict proof that a fluctuating electric field is quite strong just above each charge spot but diminishes exponentially with the distance from the plane. The lifetime τ of a charge spot is inversely proportional to the density j0 of the stochastic current while proportional to fluctuation's amplitudes independent of j0. The fluctuation's parameter dependence on the charge spot's size D can vary according to the conducting medium properties.