 Solution

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

Multiplying each ion number density by its signed charge gives the local charge density

ρ (s) = q [n_{+} (s) - n_{-} (s)] = - 2 q n_{0} sinh \frac{q ψ ( s )}{k _{B} T} .

The fixed surface charge is supplied separately as a boundary condition; it is not part of this mobile charge density in the liquid.

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