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 = dyn^1/2 cm = cm^3/2 g^1/2 s⁻¹.

Statcoulomb
Unit system	esu-cgs, Gaussian
Unit of	electrical charge
Symbol	statC or Fr, esu
Conversions
1 statC in ...	... is equal to ...
SI	10 × (ccgs)^−1 C≈3.33564×10^−10 C, where ccgs = 2.99792458×10^10 cm/s is the speed of light expressed in cgs unit.
emu-cgs	(ccgs)^−1 abC
CGS base units	1 statC = g^1/2 cm^3/2 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:

${\displaystyle F={\frac {q_{1}q_{2}}{r^{2}}}}$

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:

${\displaystyle F={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r^{2}}}}$

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 L^3/2 M^1/2 T⁻¹.

References