The problem of calculating the surface conductivity at an electrolyte-solid interface is reconsidered. Some of the limitations of the existing definitions and theoretical approaches are pointed out, and the problem is reworked to include the effects of non-zero space charge and ion concentration on the conductivity. An approximate method is presented for calculating the mobility of an ion in a non-neutral environment. These considerations are illustrated by the problem of the local conductivity in a cylindrical pipe and the local conductivity near a half plane.