Electrostatic Field of Charged Infinite Metallic Plane Contacting with Metallic Sphere

TL;DR

This paper solves the electrostatic potential problem for a charged metallic plane contacting a metallic sphere, deriving charge distributions and forces to aid in nanoparticle motion analysis and size measurement.

Contribution

It provides new analytical expressions for charge distribution and forces in the contact problem, enabling applications in nanoparticle dynamics and measurement techniques.

Findings

Derived charge density distributions on the plane and sphere

Calculated the force acting on the sphere during contact

Estimated nanoparticle shuttle frequency and charge transfer

Abstract

The problem concerning the form of the electrostatic field potential of the infinite charged metallic plane contacting with the metallic sphere is solved. The distributions of the surface charge densities both on the plane and the sphere and also the force acting on the sphere that causing to tear away from the plane are found. The expressions found for the charge of the sphere and the force of tear from the plane permits estimate the frequency of the shuttle motion of the nanoparticles and the charge transfer between metallic electrodes and also use them for the measurement of their sizes and to make use of their separation in progress.