Subtleties on energy calculations in the image method

Abstract

In this pedagogical work we point out a subtle mistake that can be done by undergraduate or graduate students in the computation of the electrostatic energy of a system containing charges and perfect conductors if they naively use the image method. Specifically, we show that the naive expressions for the electrostatic energy for these systems obtained directly from the image method are wrong by a factor 1/2. We start our discussion with well known examples, namely, point charge-perfectly conducting wall and point charge-perfectly conducting sphere and then proceed to the demonstration of general results, valid for conductors of arbitrary shapes.

9 pages, 2 figures; Major change in this version: subsection added to Sect.4 (theorem generalization). Minor changes: title replaced; corrections to the English; some explanatory comments added

Cited by in corpus (7)

• Quantum simulation of the hexagonal Kitaev model with trapped ions
• Accurate formation energies of charged defects in solids: a systematic approach
• Repulsive van der Waals interaction between a quantum particle and a conducting toroid
• Image method in the calculation of the van der Waals force between an atom and a conducting surface
• The ambivalent competition of Coulomb and van-der-Waals interactions in Xe-Cs+ aggregates on Cu(111) surfaces
• Classical theory of electron-ion correlations at electrochemical interfaces: Closing the circuit from double-layer charging to ion adsorption
• Highly excited electronic image states of metallic nanorings