# 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 (charge) | ~3.33564×10^{−10} C |

SI (flux) | ~2.65×10^{−11} C |

CGS base units | 1 statC = g^{1/2} cm^{3/2} s^{−1} |

It can be converted using

- 1 newton = 10
^{5}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 ≈ 3.00×10
^{9}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.

## 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, *q*_{1} and *q*_{2} are the two charges, and *r* is the distance between the charges. Performing dimensional analysis on Coulomb's law, the dimension of electrical charge in cgs must be [mass]^{1/2} [length]^{3/2} [time]^{−1}. (This statement is *not* true in SI units; see Gaussian units § Major differences between Gaussian and SI units). We can be more specific in light of the definition above: Substituting *F* = 1 dyn, *q*_{1} = *q*_{2} = 1 statC, and *r* = 1 cm, we get:

- 1 statC = g
^{1/2}cm^{3/2}s^{−1}

as expected.