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Michael Faraday Sticker

All Quiet In Here. | Physics

\[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]
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$4.99 USD
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Charge the box all you like. Inside, nothing. Faraday sat in a charged, foil-covered 12-foot cube and found no electrical effect: a closed conductor shields its interior. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

Gauss's law relates the electric flux through a closed surface to the charge inside it. In a closed conductor at equilibrium the charges sit on the outside, so the field in an empty cavity is zero, which is why Faraday was safe inside his charged cage.

The sticker says All Quiet In Here. Michael Faraday went and checked.

In the lecture room of the Royal Institution he set up an insulated cube twelve feet on a side: a light wooden frame strung with copper wire and covered in paper and bands of tin foil. He charged the outside until sparks and brushes darted off every part of its surface. Then he wrote: “I went into the cube and lived in it.” With lighted candles, electrometers and every other test he had, he “could not find the least influence upon them.”

The reason is that charge on a conductor moves until the whole conductor sits at one potential, and it ends up on the outer surface. In electrostatic equilibrium the field inside an empty cavity in a closed conductor is exactly zero, whatever is happening outside. Gauss's law, above, is the modern way to say it. Faraday showed it with instruments, and with himself as the test subject.

A mesh works nearly as well as solid metal, as long as the holes are small compared with the waves being blocked. That's why a microwave oven door is a mesh you can see through. It's also why a hard-topped car is a decent place to sit out a thunderstorm: the US National Weather Service notes that the outer metal shell protects the people inside with the windows closed. The rubber tyres have nothing to do with it.

The cube is usually dated to 1836, and he published it in 1838 in the eleventh series of his Experimental Researches in Electricity. Our cube is drawn smaller to fit the sticker.

The tea is our addition. The calm is his.

Equations

\[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]
\[\begin{gathered} \vec E_{\text{inside}} = 0 \\ (\text{empty cavity in a closed} \\ \text{conductor, electrostatic} \\ \text{equilibrium}) \end{gathered}\]
SymbolMeaningUnit
\(\vec E\) electric field \(\mathrm{V/m}\)
\(d\vec A\) outward area element of a closed surface S \(\mathrm{m²}\)
\(Q_{\text{enc}}\) charge enclosed by S \(\mathrm{C}\)
\(\varepsilon_0\) vacuum permittivity \(\mathrm{F/m}\)

Sources

  1. Faraday, Experimental Researches in Electricity, Series XI (1838), §1173–1174 (the cube), Vol. 1 — Project Gutenberg
  2. Encyclopaedia Britannica — Michael Faraday
  3. Wikipedia — Faraday cage
  4. US National Weather Service — Lightning and cars

Source Faraday, M. (1838). Experimental researches in electricity. — eleventh series. Philosophical Transactions of the Royal Society of London, 1–40.doi.org/10.1098/rstl.1838.0002

Field notes

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