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Edge corrections for parallel-plate capacitors

Part of: Partial differential equations Equations of mathematical physics and other areas of application Approximations and expansions Harmonic analysis in several variables Two-dimensional theory

Published online by Cambridge University Press:  30 April 2020

EHUD YARIV Open the ORCID record for EHUD YARIV [Opens in a new window]
EHUD YARIV*
Affiliation:
Department of Mathematics, Technion—Israel Institute of Technology, Haifa32000, Israel, email: udi@technion.ac.il
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Abstract

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As a result of field fringing, the capacitance of a parallel-plate capacitor differs from that predicted by the textbook formula. Using singular perturbations and conformal mapping techniques, we calculate the leading-order correction to the capacitance in the limit of large aspect ratio. We additionally obtain a comparable approximation for the electrostatic attraction between the plates.

Keywords

Singular perturbationsconformal mappings

MSC classification

Primary: 35B25: Singular perturbations 35Q60: PDEs in connection with optics and electromagnetic theory 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 31A99: None of the above, but in this section
Secondary: 42B37: Harmonic analysis and PDE
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Issue 2 , April 2021 , pp. 226 - 241
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

†

This work was supported by the Israel Science Foundation (Grant no. 1081/16).

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