Thermodynamics is applied to formulate general equations for internal energies and grand potential for a system consisting of a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. To take into account spontaneous polarization of surface layer molecules we introduce the electrical surface and line excess quantities. (C) 2013 AIP Publishing LLC.