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Reference: Hewett, DP, Trefethen, LN and Chapman, SJ, Pavliotis, G ed., (2015). Mathematics of the Faraday cage. SIAM Review, 57 (3), 398–417.Citable link to this page:


Mathematics of the Faraday cage

Abstract: The amplitude of the gradient of a potential inside a wire cage is investigated, with particular attention to the 2D configuration of a ring of n disks of radius r held at equal potential. The Faraday shielding effect depends upon the wires having finite radius and is weaker than one might expect, scaling as |log r|/n in an appropriate regime of small r and large n. Both numerical results and a mathematical theorem are provided. By the method of multiple scales, a continuum approximation is then derived in the form of a homogenized boundary condition for the Laplace equation along a curve. The homogenized equation reveals that in a Faraday cage, charge moves so as to somewhat cancel an external field, but not enough for the cancellation to be fully effective. Physically, the effect is one of electrostatic induction in a surface of limited capacitance. An alternative discrete model of the effect is also derived based on a principle of energy minimization. Extensions to electromagnetic waves and 3D geometries are mentioned.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Publisher's versionNotes:Copyright © 2015, Society for Industrial and Applied Mathematics. Citation: Chapman, S. J., Hewett, D. P., and Trefethen, L. N. (2015, January). Mathematics of the Faraday Cage. SIAM Rev. Society for Industrial and Applied Mathematics (SIAM).


Pavliotis, GMore by this contributor


 Bibliographic Details

Publisher: Society for Industrial and Applied Mathematics

Publisher Website:

Journal: SIAM Reviewsee more from them

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Issue Date: 2015


Urn: uuid:aeacd580-d66f-407d-8a2f-b0c74e41a2a0

Source identifier: 514467

Eissn: 1095-7200


Issn: 0036-1445 Item Description

Type: Journal article;

Version: Publisher's versionKeywords: Faraday cage shielding screening homogenization harmonic function Tiny URL: pubs:514467


Author: Hewett, DP - institutionUniversity of Oxford Oxford, MPLS, Mathematical Inst - - - Trefethen, LN - institutionUniversity of Oxfor



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