Statcoulomb

The franklin (Fr), statcoulomb (statC), or electrostatic unit of charge (esu) is the physical unit 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

1 statC = 1 dyn1/2⋅cm = 1 cm3/2⋅g1/2⋅s−1.
statcoulomb
Unit systemGaussian, CGS-ESU
Unit ofelectrical charge
SymbolFr, statC, esu
Derivationdyn1/2⋅cm
Conversions
1 Fr in ...... is equal to ...
   CGS base units   1 cm3/2⋅g1/2⋅s−1
   SI (charge)   ≘ ~3.33564×10−10 C
   SI (flux)   ≘ ~2.65×10−11 C

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 using

1 newton = 105 dyne
1 cm = 10−2 m

The SI system of units uses the coulomb (C) instead. The conversion between C and statC is different in different contexts. The most common contexts are:

  • For electric charge:
    1 C ≘ 2997924580 statC ≈ 3.00×109 statC
    ⇒ 1 statC ≘ ~3.33564×10−10 C.
  • For electric flux (ΦD):
    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 10 times the numeric value of the speed of light expressed in metres/second, and the conversions are exact except where indicated. The second context implies that the SI and CGS units for an electric displacement field (D) are related by:

1 C/m2 ≘ 4π × 2997924580×10−4 statC/cm2 ≈ 3.77×106 statC/cm2
⇒ 1 statC/cm2 ≘ ~2.65×10−7 C/m2

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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