Elementary charge

In the centimetre–gram–second system of units (CGS), the corresponding quantity is 4.8032047...×10−10 statcoulombs.

[b] Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%.

[4][5] Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from blackbody spectra by Max Planck in 1901[6] and (through the Faraday constant) at order-of-magnitude accuracy by Johann Loschmidt's measurement of the Avogadro number in 1865.

Later, the name electron was assigned to the particle and the unit of charge e lost its name.

However, the unit of energy electronvolt (eV) is a remnant of the fact that the elementary charge was once called electron.

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

Paul Dirac argued in 1931 that if magnetic monopoles exist, then electric charge must be quantized; however, it is unknown whether magnetic monopoles actually exist.

[9][10] It is currently unknown why isolatable particles are restricted to integer charges; much of the string theory landscape appears to admit fractional charges.

[11][12] The elementary charge is exactly defined since 20 May 2019 by the International System of Units.

Prior to this change, the elementary charge was a measured quantity whose magnitude was determined experimentally.

The value of the Avogadro constant NA was first approximated by Johann Josef Loschmidt who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas.

The value of F can be measured directly using Faraday's laws of electrolysis.

[14] In an electrolysis experiment, there is a one-to-one correspondence between the electrons passing through the anode-to-cathode wire and the ions that plate onto or off of the anode or cathode.

Measuring the mass change of the anode or cathode, and the total charge passing through the wire (which can be measured as the time-integral of electric current), and also taking into account the molar mass of the ions, one can deduce F.[1] The limit to the precision of the method is the measurement of F: the best experimental value has a relative uncertainty of 1.6 ppm, about thirty times higher than other modern methods of measuring or calculating the elementary charge.

[15] A famous method for measuring e is 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.

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. The necessity of measuring the size of the oil droplets can be eliminated by using tiny plastic spheres of a uniform size.

The force due to viscosity can be eliminated by adjusting the strength of the electric field so that the sphere hovers motionless.

By carefully analyzing the noise of a current, the charge of an electron can be calculated.

This method, first proposed by Walter H. Schottky, can determine a value of e of which the accuracy is limited to a few percent.

[16] However, it was used in the first direct observation of Laughlin quasiparticles, implicated in the fractional quantum Hall effect.

Presently this equation reflects a relation between ε0 and α, while all others are fixed values.