Finite‐Point Electrostatic Representation of Spherical and Non‐Spherical Charged Particles

ABSTRACT A finite‐point electrostatic framework is presented for representing spherical and non‐spherical charged particles as discrete charge distributions with arbitrary geometries. Rather than approximating an extended charged body as an idealized point source, the total charge is redistributed among a finite set of sub‐elements whose spatial arrangement defines the particle morphology. The formulation preserves the classical Coulomb‐superposition formalism while introducing controllable spatial structure capable of approximating continuous charge densities and finite‐size charge distributions. Five representative geometries are considered, including cubic, spherical, Fibonacci‐sphere, cylindrical, and toroidal configurations. The methodology is implemented within the Excel‐ScienSolar computational environment, where the governing electrostatic equations are introduced directly through spreadsheet cells rather than hard‐coded routines, allowing dynamic redefinition of field and potential models without modifying the source code. Validation against analytical solutions demonstrates excellent agreement in both near‐field and far‐field regimes, while convergence analyses quantify the influence of discretization level and particle geometry on numerical accuracy. The results show that isotropic charge distributions rapidly converge toward the continuous Coulomb‐integral limit, whereas anisotropic geometries preserve directional signatures in the electrostatic potential and electric field at intermediate distances. The proposed framework provides a flexible approach for investigating geometry‐dependent electrostatic interactions in systems composed of finite‐size charged particles, bridging ideal point‐charge descriptions and extended charge‐density representations.