On equilibrium charge distribution above dielectric surface

TL;DR

This paper analyzes the equilibrium charge distribution above a dielectric surface, considering external fields and surface inhomogeneities, providing solutions for charge and electric field configurations in various scenarios.

Contribution

It presents a comprehensive formulation and solutions for equilibrium charge distributions above dielectric surfaces, including effects of surface inhomogeneities and external fields.

Findings

Derived equilibrium charge distributions with and without external fields.

Solved electrostatic equations for ideal and inhomogeneous dielectric surfaces.

Analyzed effects of surface waviness and charge inhomogeneity on charge distribution.

Abstract

The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium distributions of charges and the electric field, which is generated by these charges in the system in the case of ideally plane dielectric surface, are obtained. The solution of electrostatic equations of the system under consideration in case of small spatial heterogeneities caused by the dielectric surface, is also obtained. These spatial inhomogeneities can be caused both by the inhomogeneities of the surface and by the inhomogeneous charge distribution upon it. In particular, the case of the .wavy. spatially periodic surface is considered taking into account the possible presence of the surface charges.