The dependence of the electric potential on the absorption and scattering of light by small particles has emerged as an interesting research topic, as the unexpected amplified optical signatures of a system of electrically charged particles were satisfactory predicted recently for homogeneous, uniformly charged spheres. However, natural particles are rarely of spherical shape. A comprehensive understanding of how arbitrarily shaped, charged particles interact with electromagnetic radiation has been missing. The approach we present here attempts to fill this gap by introducing a numerical formulation of the electromagnetic scattering problem for these particles. The first results from the intercomparison of numerical and analytical solutions for a pseudosphere show that the resonance features found are largely consistent, except for the magnitude and width of the peak amplitude, which may be due to inherent differences in the approaches used.