On the Electrostatic Interaction between Point Charges due to Dielectrical Shielding

TL;DR

This paper investigates how dielectric shielding affects electrostatic interactions between point charges, providing a comprehensive solution using the method of images and deriving analytical results for special cases.

Contribution

It introduces a general approach to calculate electrostatic interactions with dielectric shielding using superposed image charges, including analytical solutions for specific scenarios.

Findings

Derived a general solution for electrostatic interactions with dielectric slabs.

Obtained analytical expressions in special cases.

Highlighted the complexity of electrostatic problems with dielectric interfaces.

Abstract

How will the electrostatic interaction between two point charges change if they are shielded from the other by a dielectrical slab? While the physical setting of this electromagnetic problem is relatively simple, it is easy to be wronged and the correct solution is surprisingly complicated. Here we will show a general answer using the method of images, in which the electrical field are not found by solving the Poisson's equation but by superposing an infinite number of image charges to recurrently satisfy all interfaces' boundary conditions. We also obtain analytical and algebraic results in some special cases.