# A Nugget of Electrons

A very long while ago, I mentioned in a post that it would probably be very bad news to collect all the electrons from a bucket of water and stick them together into a little nugget. And now, I’ve finally found the equations that will tell me exactly how bad an idea that would be.

But first, let’s specify just how much water we’re dealing with. Because I live in the United States, where we frown on convenient units of measurement, I’m going to be working with a five-gallon bucket (18.93 liters). That works out to 1,050 moles of water, or about 6.323e26 water molecules. Each water molecule contains two hydrogen atoms, contributing one electron each, and one oxygen atom, contributing eight. Therefore, we have ten electrons per molecule, or 6.323e27 electrons in five gallons of water. Each electron carries a charge of about -1.602e-19 Coulombs. So, how much energy would be required to squeeze that much charge into a sphere 1 centimeter in diameter? Fortunately, the equation for this isn’t as terrifying as I expected. It goes something like this

(1/(4 * pi * vacuum permittivity)) * (3/5) * ((total charge^2)/(radius)) [1]

Sticking the values we have into the ever-trusty WolframAlpha, we get 1.11e28 Joules. That’s in the neighborhood of one hundred thousand times the kinetic energy of the asteroid that caused the KT extinction, which killed all the non-avian dinosaurs.

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