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Physics · Ch 10 — Electrostatics

Quantization of Charge

10.3.2

Quantization of Charge

Careful experiments -- most famously Millikan's oil-drop experiment -- established that charge cannot take on just any arbitrary value: there exists a smallest possible unit of charge, the ELEMENTARY CHARGE e=1.6×10−19e=1.6\times10^{-19} C, and every charge found on an object in nature is always an exact integer multiple of this elementary unit, written q=±neq=\pm ne where n is a whole number (positive, negative, or zero). This restriction to whole-number multiples is called the QUANTIZATION of charge, or the discrete nature of charge.

The underlying reason is simple: protons (each carrying +e+e) and electrons (each carrying −e-e) are the fundamental charged constituents of ordinary matter, and any charging process -- friction, contact, induction -- works by transferring some whole number of ELECTRONS from one body to another. Since electrons cannot be split into fractions, the net charge gained or lost by any object must always come out to an exact integer multiple of e. …

Misc Ex.1Example 10.1: Positive/negative charge and number of electrons in 1 gram of water

Worked out. Given water's molecular mass is 18.0 g, so 18.0 g of water contains Avogadro's number (6.02×10236.02\times10^{23}) of molecules, hence 1 g contains 6.02×1023/18≈3.34×10226.02\times10^{23}/18\approx3.34\times10^{22} molecules. Each H2OH_2O molecule has 10 electrons (2 from its two hydrogen atoms plus 8 from its one oxygen atom), so the number of electrons (equal to the number of protons, since water is neutral) in 1 g of water is 3.34×1022×10≈3.34×10233.34\times10^{22}\times10\approx3.34\times10^{23}. Multiplying by the elementary charge, total positive charge =3.34×1023×1.6×10−19C≈5.35×104=3.34\times10^{23}\times1.6\times10^{-19}\text{C}\approx5.35\times10^4 C, exactly balanced by an equal magnitude of negative charge so the water sample as a whole stays electrically neutral -- illustrating just how enormous the amount of charge locked up (but perfectly …

Misc DYK.2Do you know? -- Quarks and the fractional-charge refinement

Worked out. Modern particle physics holds that protons and neutrons are themselves built from more fundamental particles called quarks, of six distinct types (flavours), each carrying a FRACTIONAL charge of either −13e-\frac{1}{3}e or +23e+\frac{2}{3}e; a proton or a neutron is a bound combination of exactly three quarks. Crucially, this does not break the quantization of charge observed on free particles -- quarks are always confined in bound states and no free (isolated) quark has ever been observed -- it only means the truly fundamental step size of charge is e/3e/3 rather than ee, a refinement invisible at the everyday, free-particle level. The box also notes that in very sensitive modern devices, such as the single-electron transistor, the discrete, one-electron-at-a-time nature of charge CAN …