Statcoulomb
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The statcoulomb (statC), franklin (Fr), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. In terms of the Gaussian base units, it is Template:Block indent
That is, it is defined so that the proportionality constant in Coulomb's law using CGS-ESU quantities is a dimensionless quantity equal to 1.
Definition and relation to CGS base unitsEdit
Coulomb's law in the CGS-Gaussian system takes the form <math display="block">F = \frac{q_1^{_\text{G}} q_2^{_\text{G}}}{r^2} ,</math> where F is the force, qTemplate:Su and qTemplate:Su are the two electric charges, 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 Template:Val, the force of mutual electrical repulsion is 1 dyne.<ref>Template:Citation</ref> Substituting F = 1 dyn, qTemplate:Su = qTemplate:Su = 1 statC, and r = 1 cm, we get: Template:Block indent
From this it is also evident that the quantity dimension of electric charge as defined in the CGS-ESU and Gaussian systems is Template:Gaps.
Conversion between systemsEdit
Conversion of a quantity to the corresponding quantity of the International System of Quantities (ISQ) that underlies the International System of Units (SI) by using the defining equations of each system.
The SI uses the coulomb (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:<ref>Template:Cite book</ref>
- For electric charge:Template:Block indentTemplate:Block indent
- For electric flux (Template:Math):Template:Block indentTemplate:Block indent
- For electric flux density (Template:Math):Template:Block indentTemplate:Block indent
The symbol "≘" ('corresponds to') is used instead of "=" because the two sides cannot be equated.