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Electrostatic energy of polygonal charge distributions

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Abstract

An asymptotic series for the electrostatic energy \({\mathcal{E}_1(N)}\) of an N-gonal charge distribution, i.e., a set of unit charges occupying vertices of a regular N-gon with a unit circumradius, is derived. Application of Padé approximants to truncations of this expansion produces compact approximate formulae capable of estimating \({\mathcal{E}_1(N)}\) with great accuracy. A closed-form expression for the energy of electrostatic interaction of two polygonal charge distributions is obtained from the respective Fourier series. The availability of this expression allows for a rapid calculation of the relevant energy with computational effort independent of the numbers of particles involved.

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Authors and Affiliations

  1. Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451, Szczecin, Poland

    Jerzy Cioslowski & Joanna Albin

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  1. Jerzy Cioslowski
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  2. Joanna Albin
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Correspondence to Jerzy Cioslowski.

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Cioslowski, J., Albin, J. Electrostatic energy of polygonal charge distributions. J Math Chem 50, 1378–1385 (2012). https://doi.org/10.1007/s10910-012-9975-z

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  • DOI: https://doi.org/10.1007/s10910-012-9975-z

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