# Mathematics of the Faraday cage, or why is it so hard to see into your microwave oven?

## Prof. Nick Trefethen, Mathematical Institute and Balliol College

Since Faraday in 1836, wire meshes have been used to shield electrostatic and electromagnetic fields. The mathematics starts from the Laplace equation, and it must be well understood and in lots of textbooks, right?

No! Amazingly, almost no books attempt an explanation of the Faraday cage. One that does is the Feynman Lectures on Physics, vol. 2, and Feynman’s explanation is wrong, a misconceived argument leading to the invalid conclusion the Faraday shielding is exponentially effective. In this talk we’ll see that the shielding is actually much weaker than this (which is why the glass door of your microwave oven has so much metal in it). This is joint work with Jon Chapman and Dave Hewett, presented in the current issue of SIAM Review.