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Mathematics of the Faraday cage

Banff International Research Station for Mathematical Innovation and Discovery

Everybody has heard of the Faraday cage e↵ect, in which a wire mesh does a good job of blocking electric fields. Surely the mathematics of such a famous and useful phenomenon has been long ago worked out and written up in the textbooks? It seems to be not so. One reason may be that that the e↵ect is not as simple as one might expect: it depends on the wires having finite radius. Nor is it as strong as one might imagine: the shielding improves only linearly as the wire spacing decreases. This talk will present results by Jon Chapman, Dave Hewett and myself including (a) numerical simulations, (b) a theorem proved by conformal mapping, (c) a continuous model derived by multiple scales analysis, (d) a discrete model derived by energy minimization, (e) a connection with the periodic trapezoidal rule for analytic integrands, and (f) a physical explanation.

Mathematics; Functions of a complex variable; Numerical analysis; Applied analysis / inverse problems

video/mp4

Author affiliation: University of Oxford

2015-07-20

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/54103

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/