Potential distribution around cylindrical surfaces

We calculate the self-atmosphere potential of an ion near the planar surface. Imagine a planar uncharged plate in contact with a solution of general electrolytes composed of N ionic mobile species of valence z, and bulk concentration (number density) nf (i=l,2,. . . , N) (Fig. 3.10). Let and p, respectively, be the relative permittivities of the electrolyte solution and the plate. Consider the potential distribution around an ion. By symmetry, we use a cylindrical coordinate system r(s, x) with its origin 0 at the plate surface and the x-axis perpendicular to the surface. 

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