 Solution

ID: past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2006/section-a/a3/c/i/solution

n_{+} (s) = n_{0} e^{- q ψ (s) / (k_{B} T)}, n_{-} (s) = n_{0} e^{q ψ (s) / (k_{B} T)} .

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.

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