Past exam of the quantum condensed matter course of the University of Cambridge / 2006 / Section A / A3 / c / Solution

Distinguish the fixed surface charge density ${\sigma }_s$ from the mobile-ion charge magnitude $q=Ze>0$. Let $n_0$ be the bulk number density of each species in a symmetric $Z:Z$ electrolyte, choose bulk potential zero, and write $\epsilon ={\epsilon }_0{\epsilon }_r$. This convention removes the ambiguity between the surface charge and ion valence in the wording.