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

Constancy of each ionic electrochemical potential gives the Boltzmann distribution in the local electric potential:Positive potential repels positive ions and attracts negative counterions. The coordinate $s$ measures distance from a locally planar surface; the same local relations hold for a spherical potential with its appropriate radial coordinate.