Head of a Pin

What is the smallest amount of charge that can sit on the head of a pin? Some people say that the smallest non-vanishing amount of charge should be +e or –e, where e is the fundamental unit of electrical charge. What do you say?

Answer

Experiments show surprising results. Any fraction of the fundamental charge, such as +0.5 e or –0.1 e, can exist on the head of a pin! The conceptual argument goes as follows. The metal pin is an electrical conductor. In general, an electric current flows in the conductor because some free electrons move through the lattice of atomic nuclei. Any particular volume of the conductor has virtually no charge because the negative charges are balanced by the positive charges of the nuclei.

So the important physical quantity is not the electric charge in any given volume but instead how much charge has been carried through the conductor that is, the “transferred charge,” which can have any value, even a fraction of the charge of a single electron. This “transferred charge” is proportional to the sum of the shifts of all the electrons with respect to the lattice of nuclei. These electrons in the conductor can be shifted as little or as much as desired, so the sum can change continuously, and therefore so can the “transferred charge.” The pinhead can have any charge value, not just integer multiples of the fundamental charge.

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