In Part I of this work, using a one-dimensional (1D) representation of the two-dimensional (2D) electrostatic and ion concentration fields, we showed that highly selective adhesion can be achieved between two charged surfaces separated by an electrolyte. In Part II of this work, we provide a detailed theoretical justification of our 1D model by solving the electrostatic problem in a 2D configuration. We establish the conditions under which a 1D approximation is accurate in terms of material and geometrical parameters. We provide the full 2D solution that can be used to analyze other physical phenomena involving migration and separation of particles under the influence of fixed surface charges.