The statcoulomb (statC), franklin (Fr), or electrostatic unit of charge (esu) is the

unit of measurement A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other qua ...

for

electrical charge Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...

used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and

Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

systems of units. In terms of the Gaussian base units, it is That is, it is defined so that the proportionality constant in

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...

using CGS-ESU quantities is a dimensionless quantity equal to 1.

Definition and relation to CGS base units

in the CGS-Gaussian system takes the form

F = \frac ,

where ''F'' is the force, ''q'' and ''q'' are the two

electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...

s, and ''r'' is the distance between the charges. This serves to define charge as a quantity in the Gaussian system. The statcoulomb is defined such that if two electric charges of 1 statC each and have a separation of , the force of mutual electrical repulsion is 1

dyne The dyne (symbol: dyn; ) is a derived units of measurement, unit of force (physics), force specified in the centimetre–gram–second system of units, centimetre–gram–second (CGS) system of units, a predecessor of the modern International S ...

. Substituting ''F'' = 1 dyn, ''q'' = ''q'' = 1 statC, and ''r'' = 1 cm, we get: From this it is also evident that the quantity dimension of electric charge as defined in the CGS-ESU and Gaussian systems is .

Conversion between systems

Conversion of a quantity to the corresponding quantity of the

International System of Quantities The International System of Quantities (ISQ) is a standard system of Quantity, quantities used in physics and in modern science in general. It includes basic quantities such as length and mass and the relationships between those quantities. This ...

(ISQ) that underlies the

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

(SI) by using the defining equations of each system. The SI uses the

coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second, with the elementary charge ''e'' as a defining c ...

(C) as its unit of electric charge. The conversion factor between corresponding quantities with the units coulomb and statcoulomb depends on which quantity is to be converted. The most common cases are: * For

: * For

electric flux In electromagnetism, electric flux is the total electric field that crosses a given surface. The electric flux through a closed surface is directly proportional to the total charge contained within that surface. The electric field E can exert ...

(): * For

electric flux density In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, comb ...

(): The symbol "≘" ('corresponds to') is used instead of "=" because the two sides cannot be equated.

References

{{reflist Units of electrical charge Centimetre–gram–second system of units