The elementary charge, usually denoted e,^[1] is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. This is a fundamental physical constant.

It has a measured value of approximately 1.602 176 487(40) × 10^–19 coulombs^[2] In cgs, the value is 4.803 204 27(12) × 10^–10 statcoulombs^[3] In the system of atomic units as well as some other systems of natural units, e functions as the unit of electric charge, i.e. e = 1 in those unit systems.

The magnitude of the elementary charge was first measured in Robert Millikan's famous oil-drop experiment in 1909.

Experimental measurements of the elementary charge

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Oil-drop experiment

Main article: Oil-drop experiment

The original method for measuring e was Millikan's oil-drop experiment. A small drop of oil in an electric field would move at a rate that balanced the forces of gravity, viscosity (of traveling through the air), and electric force. The forces due to gravity and viscosity could be calculated based on the size and velocity of the oil drop, so electric force could be deduced. Since electric force, in turn, is the product of the electric charge and the known electric field, the electric charge of the oil drop could be accurately computed. By measuring the charges of many different oil drops, it can be seen that the charges are all integer multiples of a single small charge, namely e.

Shot noise

Main article: Shot noise

Any electric current will be associated with noise from a variety of sources. One of these sources, shot noise, is due to the fact that the current is not a smooth continual flow, but rather consists of discrete electrons which pass through one at a time. By carefully analyzing the noise of a current, the charge of an electron can be calculated. This method can give a value of e accurate to a few percent.^[4]

Charge quantization

Charge quantization is the statement that every particle or object has a charge which is an integer multiple of the elementary charge e: A charge can be exactly 0, or exactly e, -e, 2e, etc., but not, say, half of e, or -3.8 times e, etc. (This statement must be interpreted carefully; see below for more details.)

This is the reason for the terminology "elementary charge": It is meant to imply that it is an indivisible unit of charge.

Charges less than an elementary charge

There are two known sorts of exceptions to the indivisibility of the elementary charge: quarks and quasiparticles.

• Quarks, first posited in the 1960s, have quantized charge, but the charge is quantized into multiples of ¹⁄₃ e. However, quarks cannot be seen as isolated particles; they only exist in groupings, and stable groupings of quarks (such as a proton, which consists of three quarks) all have charges that are integer multiples of e. For this reason, either e or ¹⁄₃ e can be justifiably considered to be "the quantum of charge", depending on the context.

• Quasiparticles are not particles as such, but rather an emergent entity in a complex material system that behaves like a particle. In 1982 Robert Laughlin tried to explain the fractional quantum Hall effect by postulating the existence of fractionally charged quasiparticles. This theory is now widely accepted, but this is not considered to be a violation of the principle of charge quantization, since quasiparticles are not elementary particles.

References

• Fundamentals of Physics, 7th Ed., Halliday, Robert Resnick, and Jearl Walker. Wiley, 2005