Is Feynman's Analysis of Electrostatic Screening Correct?

TL;DR

This paper defends Feynman's analysis of electrostatic shielding against recent criticisms, demonstrating that his Green's function approach remains valid for wires of finite thickness and clarifying misconceptions about the boundary conditions involved.

Contribution

It clarifies that Feynman's original analysis is correct by interpreting his solution as a Green's function applicable to wires of finite thickness with proper boundary conditions.

Findings

Feynman's solution is a valid Green's function for finite-thickness wires.

The analogy to a parallel plate capacitor aids understanding of Feynman's argument.

The behavior of a finite ring of wires differs from Feynman's original case, showing no exponential screening.

Abstract

In a recent paper on electrostatic shielding, Chapman, Hewett and Trefethen present arguments that the analysis of this effect by Feynman is incorrect. Feynman analyzed shielding by a row of infinitesimally thin wires. They claim that Feynman used the wrong boundary conditions invalidating his analysis. In this paper we emphasize that Feynman's solution is a Green's function through which behavior of the potential due to finite thickness wires of arbitrary cross-section with appropriate boundary condition can be understood. This shows that the main conclusions of Feynman's treatment are indeed correct. Analogy to a parallel plate capacitor with one of the plates replaced by a row of wires provides a more intuitive understanding of Feynman's argument. The case of a finite number of wires arranged in a ring (not treated by Feynman), as a model of Faraday cage, is different. The structure of the solution in radial coordinates already suggests that one should not expect exponential behavior and further analysis confirms this. There appear to be contradictory results in the literature for its screening behavior in the presence of external charges or fields.