Analysis of infinite plane assumption and point charge assumption in the particle–plane electrostatic interaction model by re-expansion method and image multipole method

The solutions for the electrostatic interacting force between a particle and a plane typically assume that the plane is infinite and the particle can be approximated as a point charge. Nevertheless, the prerequisites of underlying assumptions of these calculations remain unspecified, resulting in the inability to assess the reliability of the results and constraining the practical applicability of analytical models. In this paper, the authors introduce the particle–coated plane electrostatic interaction model by employing the re-expansion method. Additionally, the multipole–coated plane electrostatic interaction model is presented using the image multipole method. An analysis of the assumptions’ prerequisites is conducted, considering a relative error of less than 2 % as the approximate standard. The findings indicate that, irrespective of the material properties of the particle and plane, the radius of the planar plate must exceed three times the distance between the particle's center and the plane to satisfy the infinite plane assumption. When the distance between the particle's center and the plane surpasses three times the radius, it is permissible to approximate the charged particle as a point charge. The study presented in this paper establishes a standard for prior estimation of the departure range in existing analytical models related to particle–plane electrostatic interaction. This work also serves as a theoretical basis for the practical application of these models in engineering.