Statcoulomb

In physics, a statcoulomb (symbol statC), formerly known as esu of charge, is the unit of electric charge in the cgs-esu (centimeter-gram-second electrostatic system) of units.

By definition, a point charge has magnitude one statcoulomb if it repels a point charge of equal magnitude at a distance of 1 centimeter with a force of one dyne.

1 statC = 1 esu of charge = C/(10⋅c) ≈ 3.335 640 95⋅10⁻¹⁰ C

where C (coulomb) is the SI unit of charge and c is the SI speed of light (c ≈ 3⋅10⁸ m/s).

Conversion to coulomb

The conversion of statC to C can be done as follows. Write

1 C = k statC,

and compute k. Consider two charges of 1 C each, 1 m apart, then the force between them is according to Coulomb's law in SI units,

$F={\frac {1}{4\pi \varepsilon _{0}}}=10^{-7}c^{2}\quad {\textrm {[N]}}$

(see electric constant for the SI value of ε₀). The same system of two charges has in cgs units a force in dyne (1 dyn = 10⁻⁵ N):

$F'={\frac {k^{2}}{100^{2}}}\;\Longrightarrow \;F'=10^{-4}k^{2}\quad {\textrm {[dyn]}}\;\Longrightarrow \;F'=10^{-9}k^{2}\quad {\textrm {[N]}},$

where we applied Coulomb's law in electrostatic units. Hence

$10^{-9}k^{2}=10^{-7}c^{2}\;\Longrightarrow \;k=10c.$