Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2018/paper-2/section-a-iii/16/iii/solution

Take a positive surface potential , so positive ions are co-ions and negative ions counterions. With ,
The counterion density is slightly enhanced at the surface, the co-ion density slightly depleted, and both approach over a Debye length. To first order their sum is , while their difference supplies the screening charge. Reverse the surface sign and the ionic roles interchange. These are number-density profiles, not trajectories of individual ions.

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