Theoretical assessment of the disparity in the electrostatic forces between two point charges and two conductive spheres of equal radii

TL;DR

This paper theoretically evaluates the difference between Coulomb's point charge force and the actual electrostatic force between two conductive spheres of equal radii, considering their size, shape, and charge distribution.

Contribution

It provides a generalized assessment of electrostatic force disparity for conductive spheres, extending Coulomb's law to real-world geometries and distances.

Findings

Force disparity is significant at short distances.

Electrostatic force decreases rapidly with increasing distance.

Force becomes negligible at large separations.

Abstract

The Coulomb's formula for the force FC of electrostatic interaction between two point charges is well known. In reality, however, interactions occur not between point charges, but between charged bodies of certain geometric form, size and physical structure. This leads to deviation of the estimated force FC from the real force F of electrostatic interaction, thus imposing the task to evaluate the disparity. In the present paper the problem is being solved theoretically for two charged conductive spheres of equal radii and arbitrary electric charges. Assessment of the deviation is given as a function of the ratio of the distance R between the spheres centers to the sum of their radii. For the purpose, relations between FC and F derived in a preceding work of ours, are employed to generalize the Coulomb's interactions. At relatively short distances between the spheres, the Coulomb force FC, as estimated to be induced by charges situated at the centers of the spheres, differ significantly from the real force F of interaction between the spheres. In the case of zero and non-zero charge we prove that with increasing the distance between the two spheres, the force F decrease rapidly, virtually to zero values, i.e. it appears to be short-acting force.