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 systemesu-cgs, Gaussian
Unit ofelectrical charge
SymbolstatCorFr, 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

The SI unit of charge is the coulomb (C). The conversion between C and statC is:

  • 1 C = 2997924580 statC3.00×109 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

as expected.

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