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centimeter-gram-second electrostatic
system of units

Symbol, esu. In this system an electric unit was provided by describing the size of a charge in terms of a force. If you have ever attracted or repelled with a comb rubbed against your clothing, you have observed a force acting between charged bodies.

Imagine two bodies with electric charges, Q₁ and Q₂ respectively. Coulomb's Inverse Square Law for electrostatic charges describes the force between them:

where F is the force, r is the distance (which has to be considerably larger than the bodies themselves), and ε (epsilon) is what is called the permittivity of the medium between the charges.

In the cgs system force is in dynes. The dyne has the base units

,

so let r be in centimeters. To define the unit of charge in the cgs electrostatic system of units, ε is disposed of by defining its value as equal to 1 for a vacuum. Inserting the other dimensions into Coulomb's law, the base units of the unit of charge are seen to be:

This unit is called the esu unit of charge, the electrostatic unit of charge, or the statcoulomb. All the other esu units are defined in terms of the esu unit of charge and the centimeter, gram and second. To distinguish cgs electrostatic units from units in the international system, they were sometimes given the prefix “stat-”.

In the revision of the SI system in 2019 the CGPM adopted a fixed value for the elementary unit of charge, e, and let the value of the magnetic permeability of the vacuum, previously fixed, be determined experimentally. In the cgs electrostatic system e is determined experimentally, and the vacuum magnetic permeability is fixed, which is how it used to be in SI. The changes made the conversion factors previously used for converting units in the electrostatic cgs system to SI units obsolete. See Stock et al, page 7.

Michael Stock, Richard Davis, Estefanía de Mirandés and Martin J. T. Milton.
The revision of the SI—the result of three decades of progress in metrology.
Metrologia vol. 56, no. 2 (22 February 2019) 022001
https://doi.org/10.1088/1681-7575/ab0013

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Last revised: 4 April 2019.