Abstract <p>Electric charging of the surfaces of airless cosmic bodies is caused by the action of the solar wind plasma and the solar UV radiation. In the present paper it is investigated how the dielectric permittivity of the surface layer of small cosmic bodies (asteroids, dwarf planets) influences their surface charging (and hence charging of dust grains on the surface). We show theoretically that this dielectric permittivity in some regions provides significantly stronger charging of the surface than it was estimated earlier. In relation with this it is investigated how the layer with the frozen water under the surface influences charging of dust grains.</p>