Mathematics of the Faraday Cage

Thursday, April 30, 2015 -
12:00pm to 1:00pm
WID 3280B

Speaker Name: 

Professor Nick Trefethen

Speaker Institution: 

University of Oxford

Cookies: 

No

Description: 

Everybody has heard of the Faraday cage effect, in which a wire mesh does a good job of blocking electric fields an electromagnetic waves. 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, and indeed, one of the few treatments to be found in the textbooks, by Feynman, is incorrect. The shielding effect turns out to be not as simple as one might expect: it depends on the wires having finite radius. Nor is it as strong as one might imagine: it improves only linearly as thewire spacing decreases. This talk will present results on electrostatic Faraday shielding by Jon Chapman, Dave Hewett and myself, to appear in SIAM Review. Mathematically, this is a problem of harmonic measure. Physically, Faraday shielding cage can be regarded an electrostatic induction by a surface of limited capacitance.