= Solution
The particle carries positive <surface charge density> $\sigma=Q/(4\pi a^2)$. Its surrounding <electric double layer> has an excess of negative <chloride> <counterions> and a deficit of positive <magnesium> <coions>. Thus $\phi(r)>0$ decreases to zero, $n_{\mathrm{Cl}}(r)$ decreases towards its bulk value, and $n_{\mathrm{Mg}}(r)$ increases towards its bulk value. The diffuse <charge density> is negative and tends to zero.
If $c$ denotes the bulk number of dissolved salt formula units per unit volume, the far-field <number densities> are $n_{\mathrm{Mg},\infty}=c$ and $n_{\mathrm{Cl},\infty}=2c$. The bulk is neutral even though these number densities differ. In the dilute mean-field picture the total diffuse <electric charge> is $-Q$, ensuring overall <electroneutrality>. A molecularly bound compact layer would require additional surface-chemistry information and is not assumed in the supplied potential.
\Image[/past-exam-of-the-soft-condensed-matter-course-of-the-university-of-cambridge/2022-q6-ion-cloud.png]
{title=<Counterion> enrichment and <coion> depletion around a positive sphere}
{description=Original schematic. The left panel distinguishes the positive surface from an excess of chloride in the surrounding diffuse cloud; symbol positions are illustrative. The right panel plots the mean-field concentrations normalized separately to their bulk values, for a small illustrative positive surface potential. Both normalized curves tend to one, although bulk chloride number density is twice bulk magnesium number density.}
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