Mean charge  ⟨ Z ⟩  and the standard deviation associated with two different dust topologies as a function of the orbital radius R with |Ṁ_d| = 10^-10   M_∗   yr^-1. The profiles shown in the left panel refer to BCCA agglomerates with N = 10⁶ (top), N = 10⁴ (middle), and N = 10² (bottom) monomers of a₀ = 10^-5   cm. The results obtained for the corresponding compact spheres are shown in the right panel. Here, the radius a_∗ of the compact sphere varies from a_∗ = 10^-3   cm (top) to a_∗ = 4.64 × 10^-5   cm (bottom) passing a_∗ = 2.15 × 10^-4   cm. The lines correspond to the values obtained by numerical integration while the values marked by (blue) filled circles are obtained using the semi-analytical solution.