# Statcoulomb

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statcoulomb | |
---|---|

Unit system | esu-cgs, Gaussian |

Unit of | electrical charge |

Symbol | statC or Fr, esu |

Conversions | |

1 statC in ... | ... is equal to ... |

SI | 10 × (c_{cgs})^{−1} C≈3.33564×10^{−10} C, where c_{cgs} = 2.99792458×10^{10} cm/s is the speed of light expressed in cgs unit. |

emu-cgs | (c_{cgs})^{−1} abC |

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

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}.

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 or, in other words, the speed of light in decimeters per second.

## Definition and relation to cgs base units[edit]

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.

In SI units, the parallel statement for the force between two charges is:

where *ε*_{0} is the electric constant. The effect of the Gaussian-cgs definition is to fold the "1/4*πε*_{0}" 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}.