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We thought we understood the Faraday Cage:

The Faraday cage effect involves shielding of electrostatic and electromagnetic fields. A closed metal cavity makes a perfect shield, with zero fields inside, and that is in the textbooks. Faraday’s discovery of 1836 was that fields are nearly zero inside a wire mesh, too. You see this principle applied in your microwave oven, whose front door contains a metal screen with small holes. The screen keeps the microwaves in, while allowing light, with its much smaller wavelength, to pass through.

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So I started looking in books and talking to people and sending emails. In the books, nothing! Well, a few of them mention the Faraday cage, but rarely with equations. And from experts in mathematics, physics, and electrical engineering, I got oddly assorted explanations. They said the skin depth effect was crucial, or this was an application of the theory of waveguides, or the key point was Babinet’s principle, or it was Floquet theory, or “the losses in the wires will drive everything…”

And then at lunch one day, colleague n+1n+1 told me, it’s in the Feynman Lectures [2]! And sure enough, Feynman gives an argument that appears to confirm the exponential intuition exactly.

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Now Feynman is a god, the ultimate cool genius. It took me months, a year really, to be confident that the great man’s analysis of the Faraday cage, and his conclusion of exponential shielding, are completely wrong.

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In closing, I want to reflect on some of the curious twists of this story, first, by mentioning three lessons:

L1. There are gaps out there. If you find something fundamental that nobody seems to have figured out, there’s a chance that, in fact, nobody has.

L2. Analogies are powerful. I would never have pursued this problem had I not been determined to understand the mathematical relationship between the Faraday cage and the trapezoidal rule.

L3. Referees can be useful. Thank you, anonymous man or woman who told us the Faraday cage section in our trapezoidal rule manuscript wasn’t convincing! We removed those embarrassing pages, and proper understanding came months later.

And then three questions:

Q1. How can arguably the most famous effect in electrical engineering have remained unanalyzed for 180 years?

Q2. How can a big error in the most famous physics textbook ever published have gone unreported since 1964?

Q3. Somebody must design microwave oven doors based on laboratory measurements. Where are these people?

(Hat tips to our Slovenian guest and Ross.)

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