Editing Statcoulomb

{{Short description|CGS unit of electric charge}}

{{Refimprove|date=November 2024}}
{{Infobox unit
| name         = statcoulomb
| image        = 
| caption      = 
| standard     = [[Gaussian units|Gaussian]], [[Centimetre–gram–second system of units#Electrostatic units (ESU)|CGS-ESU]]
| quantity     = [[electric charge]]
| symbol       = Fr
| symbol2      = statC, esu
| namedafter   = 
| extralabel   = Derivation
| extradata    = dyn<sup>1/2</sup>⋅cm
| units1       = CGS base&nbsp;units
| inunits1     = 1&nbsp;cm<sup>3/2</sup>⋅g<sup>1/2</sup>⋅s<sup>−1</sup>
| units2       = [[International System of Units|SI]] (charge)
| inunits2     = ≘&nbsp;~&nbsp;{{val|3.33564|e=-10|ul=C}}
| units3       = [[International System of Units|SI]] (flux)
| inunits3     = ≘&nbsp;~&nbsp;{{val|2.65|e=-11|ul=C}}
}}

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 system of units#Electrostatic units (ESU)|centimetre–gram–second electrostatic units variant]] (CGS-ESU) and [[Gaussian units|Gaussian]] systems of units. In terms of the Gaussian base units, it is
{{block indent | em = 1.5 | text = 1&nbsp;statC = 1&nbsp;dyn<sup>1/2</sup>⋅cm = 1&nbsp;cm<sup>3/2</sup>⋅g<sup>1/2</sup>⋅s<sup>−1</sup>.}}

That is, it is defined so that the proportionality constant in [[Coulomb's law]] using CGS-ESU quantities is a dimensionless quantity equal to&nbsp;1.

== Definition and relation to CGS base units ==
[[Coulomb's law]] in the [[Gaussian units|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, ''q''{{su|b=1|p={{small|G}}|lh=0.9}} and ''q''{{su|b=2|p={{small|G}}|lh=0.9}} are the two [[electric charge]]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&nbsp;statC each and have a separation of {{val|1|u=cm}}, the force of mutual electrical repulsion is 1&nbsp;[[dyne]].<ref>{{citation |author=Jan Gyllenbok |title=Encyclopaedia of Historical Metrology, Weights, and Measures Volume 1 |publisher=Birkhauser |date=2018 |isbn=978-3-319-57598-8 |page=29 }}</ref>  Substituting ''F'' = 1&nbsp;dyn, ''q''{{su|b=1|p={{small|G}}|lh=0.9}} = ''q''{{su|b=2|p={{small|G}}|lh=0.9}} = 1&nbsp;statC, and ''r'' = 1&nbsp;cm, we get:
{{block indent | em = 1.5 | text = 1&nbsp;statC = g<sup>1/2</sup>⋅cm<sup>3/2</sup>⋅s<sup>−1</sup>.}}

From this it is also evident that the [[quantity dimension]] of electric charge as defined in the CGS-ESU and Gaussian systems is {{gaps|M<sup>1/2</sup>|L<sup>3/2</sup>|T<sup>−1</sup>}}.

== Conversion between systems ==
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>{{cite book|title = Applied Electronics |url = https://archive.org/details/Applied_Electronics_Truman_S._Gray_1954/page/830/mode/1up |at = pp. 830–831, Appendix B |first1 = Truman S. |last1 = Gray |year = 1954 |publisher = John Wiley & Sons, Inc. |location = New York }}</ref>
* For [[electric charge]]:<!--
-->{{block indent | em = 1.5 | text = 1&nbsp;C ≘ 1&nbsp;C × {{math|{{sqrt|1/4''πε''<sub>0</sub>}}}} ≈ {{val|2.99792|e=9|u=statC}}}}<!--
-->{{block indent | em = 1.5 | text = 1&nbsp;statC ≘ 1&nbsp;statC × {{math|{{sqrt|4''πε''<sub>0</sub>}}}} ≈ {{val|3.33564|e=-10|u=C}}.}}
* For [[electric flux]] ({{math|Φ<sub>D</sub>}}):<!--
-->{{block indent | em = 1.5 | text =1&nbsp;C ≘ 1&nbsp;C × {{math|{{sqrt|4''π''/''ε''<sub>0</sub>}}}} ≈ {{val|3.76730|e=10|u=statC}}}}<!--
-->{{block indent | em = 1.5 | text = 1&nbsp;statC ≘ 1&nbsp;statC × {{math|{{sqrt|''ε''<sub>0</sub>/4''π''}}}} ≈ {{val|2.65442|e=-11|u=C}}.}}
* For [[electric displacement field|electric flux density]] ({{math|'''D'''}}):<!--
-->{{block indent | em = 1.5 | text = 1&nbsp;C/m<sup>2</sup> ≘ 1&nbsp;C/m<sup>2</sup> × {{math|{{sqrt|4''π''/''ε''<sub>0</sub>}}}} ≈ {{val|3.76730|e=6|u=statC/cm<sup>2</sup>}}}}<!--
-->{{block indent | em = 1.5 | text = 1&nbsp;statC/cm<sup>2</sup> ≘ 1&nbsp;statC/cm<sup>2</sup> × {{math|{{sqrt|''ε''<sub>0</sub>/4''π''}}}} ≈ {{val|2.65442|e=-7|u=C/m<sup>2</sup>}}.}}

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

== References ==
{{reflist}}

[[Category:Units of electrical charge]]
[[Category:Centimetre–gram–second system of units]]