The statcoulomb (statC) or franklin (Fr) or electrostatic unit of charge (esu) is the physical unit for electrical charge used in the esu-cgs (centimetre–gram–second system of units) and Gaussian units. It is a derived unit given by
- 1 statC = dyn1/2 cm = cm3/2 g1/2 s−1.
|Unit system||esu-cgs, Gaussian|
|Unit of||electrical charge|
|Symbol||statC or Fr, esu|
|1 statC in ...||... is equal to ...|
|SI (charge)||~3.33564×10−10 C|
|SI (flux)||~2.65×10−11 C|
|CGS base units||1 statC = g1/2 cm3/2 s−1|
It can be converted using
- 1 newton = 105 dyne
- 1 cm = 10−2 m
- 1 C = 2997924580 statC ≈ 3.00×109 statC
- 1 statC = ~3.33564×10−10 C.
The number 2997924580 is 10 times the value of the speed of light expressed in meters/second.
Definition and relation to cgs base units
The statcoulomb is defined as follows: if two stationary objects each carry a charge of 1 statC and are 1 cm apart, they will electrically repel each other with a force of 1 dyne. This repulsion is governed by Coulomb's law, which in the Gaussian-cgs system states:
where F is the force, q1 and q2 are the two charges, and r is the distance between the charges. Performing dimensional analysis on Coulomb's law, the dimension of electrical charge in cgs must be [mass]1/2 [length]3/2 [time]−1. (This statement is not true in SI units; see Gaussian units § Major differences between Gaussian and SI units). We can be more specific in light of the definition above: Substituting F = 1 dyn, q1 = q2 = 1 statC, and r = 1 cm, we get:
- 1 statC = g1/2 cm3/2 s−1