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 $\varepsilon=\varepsilon_0\varepsilon_r$. This convention removes the ambiguity between the surface charge and ion valence in the wording.


Solution

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

 Solution (source code)