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Statcoulomb#As a unit of flux of electric displacement field

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

{{Refimprove|date=November 2024}}

{{Infobox unit

| name = statcoulomb

| image =

| caption =

| standard = Gaussian, CGS-ESU

| quantity = electric charge

| symbol = Fr

| symbol2 = statC, esu

| namedafter =

| extralabel = Derivation

| extradata = dyn1/2⋅cm

| units1 = CGS base units

| inunits1 = 1 cm3/2⋅g1/2⋅s−1

| units2 = SI (charge)

| inunits2 = ≘ ~ {{val|3.33564|e=-10|ul=C}}

| units3 = SI (flux)

| inunits3 = ≘ ~ {{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 electrostatic units variant (CGS-ESU) and Gaussian systems of units. In terms of the Gaussian base units, it is

{{block indent | em = 1.5 | text = 1 statC = 1 dyn1/2⋅cm = 1 cm3/2⋅g1/2⋅s−1.}}

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 units

Coulomb's law in the CGS-Gaussian system takes the form

F = \frac{q_1^{_\text{G}} q_2^{_\text{G}}}{r^2} ,

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 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 {{val|1|u=cm}}, the force of mutual electrical repulsion is 1 dyne.{{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 }} Substituting F = 1 dyn, q{{su|b=1|p={{small|G}}|lh=0.9}} = q{{su|b=2|p={{small|G}}|lh=0.9}} = 1 statC, and r = 1 cm, we get:

{{block indent | em = 1.5 | text = 1 statC = g1/2⋅cm3/2⋅s−1.}}

From this it is also evident that the quantity dimension of electric charge as defined in the CGS-ESU and Gaussian systems is {{gaps|M1/2|L3/2|T−1}}.

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:{{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 }}

  • For electric charge:{{block indent | em = 1.5 | text = 1 C ≘ 1 C × {{math|{{sqrt|1/4πε0}}}} ≈ {{val|2.99792|e=9|u=statC}}}}{{block indent | em = 1.5 | text = 1 statC ≘ 1 statC × {{math|{{sqrt|4πε0}}}} ≈ {{val|3.33564|e=-10|u=C}}.}}

    • For electric flux ({{math|ΦD}}):{{block indent | em = 1.5 | text =1 C ≘ 1 C × {{math|{{sqrt|4π/ε0}}}} ≈ {{val|3.76730|e=10|u=statC}}}}{{block indent | em = 1.5 | text = 1 statC ≘ 1 statC × {{math|{{sqrt|ε0/4π}}}} ≈ {{val|2.65442|e=-11|u=C}}.}}

      • For electric flux density ({{math|D}}):{{block indent | em = 1.5 | text = 1 C/m2 ≘ 1 C/m2 × {{math|{{sqrt|4π/ε0}}}} ≈ {{val|3.76730|e=6|u=statC/cm2}}}}{{block indent | em = 1.5 | text = 1 statC/cm2 ≘ 1 statC/cm2 × {{math|{{sqrt|ε0/4π}}}} ≈ {{val|2.65442|e=-7|u=C/m2}}.}}

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

References

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Category:Units of electrical charge

Category:Centimetre–gram–second system of units