Flypaper and the Faraday cage

For the first time in my life this summer, I had to buy flypaper. The fruit flies in our kitchen in Lyon were annoying. It became fascinating to watch them dart around seemingly at random, and occasionally light on the sticky paper.

Suppose they fly truly in a path of Brownian motion (in fact it’s not so simple), and suppose I had hung a ring of flypapers (in fact I hung just one). Then this would have been the same mathematics as the Faraday cage! For electric fields are governed by Laplace’s equation, just like Brownian motion.

Our analysis of the Faraday cage translates as follows to fruit flies getting through a ring of flypapers to a banana. (a) As long as there are good-sized gaps between the papers, the number of flies getting through will not be negligible (this was Feynman’s error). (b) If the papers themselves are made narrower, even down to a scale of millimeters, the effectiveness of the cage diminishes only slightly (in proportion to an inverse-logarithm of the radius). This is one of the paradoxes of Brownian paths, going back to Berg and Purcell in 1977.

[24 November 2018]