Statcoulomb

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The franklin (Fr), statcoulomb (statC), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. It is a derived unit given by

That is, it is defined so that the CGS-ESU quantity that corresponds to the Coulomb constant is a dimensionless quantity equal to 1.

It can be converted to the corresponding SI quantity using

In the International System of Units uses the coulomb (C) as its unit of electric charge. The conversion between the units coulomb and the statcoulomb depends on the context. The most common contexts are^[a]:

• For electric charge:
  1 C ≘ ~2997924580 statC ≈ 3.00×10⁹ statC
  ⇒ 1 statC ≘ ~3.33564×10⁻¹⁰ C.
• For electric flux (Φ_D):
  1 C ≘ ~4π × 2997924580 statC ≈ 3.77×10¹⁰ statC
  ⇒ 1 statC ≘ ~2.65×10⁻¹¹ C.

The symbol "≘" ('corresponds to') is used instead of "=" because the two sides are not interchangeable, as discussed below. The number 2997924580 is very close to 10 times the numeric value of the speed of light when expressed in the unit metre/second. In the context of electric flux, the SI and CGS units for an electric displacement field (D) are related by:

due to the relation between the metre and the centimetre. The coulomb is an extremely large charge rarely encountered in electrostatics, while the statcoulomb is closer to everyday charges.
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