| statcoulomb | |
|---|---|
| Unit system | esu-cgs, Gaussian |
| Unit of | electrical charge |
| Symbol | statC or Fr, esu |
| Conversions | |
| 1 statC in ... | ... is equal to ... |
| SI | 10 × (ccgs)−1 C ≈ 3.33564×10−10 C, where ccgs = 2.99792458×1010 is the speed of light expressed in cgs units. |
| emu-cgs | (ccgs)−1 abC |
| CGS base units | 1 statC = cm3/2⋅g1/2⋅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 = 1 dyn1/2⋅cm = 1 cm3/2⋅g1/2⋅s−1.
It can be converted using
- 1 newton = 105 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 ≈ 3.00×109 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
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, q1 and q2 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 ε0 is the electric constant. The effect of the Gaussian-cgs definition is to fold the "1/4πε0" 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 L3/2 M1/2 T−1.