The random walk of an electrostatic field using parallel infinite charged planes

TL;DR

This paper models a stochastic process where the electrostatic field undergoes a random walk generated by multiple parallel infinite charged planes with random charge distributions, deriving probability distributions and physical quantities.

Contribution

It introduces a novel stochastic model for electrostatic fields influenced by random charge distributions on infinite planes, using a rate equation approach.

Findings

Probability distribution of electrostatic field intensity derived

Mean electrostatic force calculated

Energy density characterized

Abstract

We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either $\pm\sigma$. We formulate the problem of this stochastic process by using a rate equation for the most probable value for the electrostatic field subject to the appropriate transition probabilities according to the electrostatic boundary conditions. Our model gives rise to a stochastic law when the charge distribution is not deterministic. The probability distribution of the electrostatic field intensity, the mean value of the electrostatic force and the energy density are obtained.