Statcoulomb

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.
Statcoulomb
Unit systemesu-cgs, Gaussian
Unit ofelectrical charge
SymbolstatC or Fr, esu 
Conversions
1 statC in ...... is equal to ...
   SI   10 × (ccgs)−1 C≈3.33564×10−10 C, where ccgs = 2.99792458×1010 cm/s is the speed of light expressed in cgs unit.
   emu-cgs   (ccgs)−1 abC
   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 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 or, in other words, the speed of light in decimeters per 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.

In SI units, the parallel statement for the force between two charges is:

where ε0 is the electric constant. The effect of the Gaussian-cgs definition is to fold the "1/4πε0" factor into the definition of the statcoulomb by setting it equal to unity in terms of length, mass, and time; which results in the Gaussian unit of electric charge possessing the cgs dimensions of L3/2 M1/2 T−1.

References
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