# Coulomb

For other uses, see Coulomb (disambiguation).
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Coulomb
Unit system SI derived unit
Unit of Electric charge
Symbol C
Named after Charles-Augustin de Coulomb
Unit conversions
1 C in ...... is equal to ...
SI base units    1 A s
CGS units    Script error: No such module "Gaps". statC
Atomic units    Script error: No such module "Gaps".[1]

The coulomb (named after Charles-Augustin de Coulomb, unit symbol: C) is the SI unit of electric charge (symbol: Q or q), defined as the charge transported by a constant current of one ampere in one second:

$1 \text{ C} = 1 \text{ A} \cdot 1 \text{ s}$

Thus it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:

$1 \text{ C} = 1 \text{ F} \cdot 1 \text{ V}$

It is equivalent to the charge of approximately 6.241×1018 protons, and −1 C is equivalent to the charge of about 6.241×1018 electrons.

## Name and notation

This SI unit is named after Charles-Augustin de Coulomb. As with every International System of Units (SI) unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (C). However, when an SI unit is spelled out in English, it should always begin with a lower case letter (coulomb), except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on The International System of Units, section 5.2.[2]

## Definition

In the SI system, the coulomb is defined in terms of the ampere and second: 1 C = 1 A × 1 s.[3] The second is defined in terms of a frequency which is naturally emitted by caesium atoms.[4] The ampere is defined using Ampère's force law;[5] the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France.[6] In practice, the watt balance is used to measure amperes with the highest possible accuracy.[6]

Since the charge of one electron is known to be about −1.602176565(35)×1019Lua error: Unmatched close-bracket at pattern character 67.,[7] −1 C can also be considered to be the charge of roughly Script error: No such module "Gaps". (or +1 C the charge of that many positrons or protons), where the number is the reciprocal of Script error: No such module "Gaps"..

The proposed redefinition of the ampere and other SI base units would have the effect of fixing the numerical value of the fundamental charge to an explicit constant expressed in coulombs, and therefore it would implicitly fix the value of the coulomb when expressed as a multiple of the fundamental charge (the numerical values of those quantities are the multiplicative inverses of each other).

## SI prefixes

#REDIRECTmw:Help:Magic words#Other
This page is a soft redirect. Common multiples are in bold face.
 Submultiples Multiples Value Symbol Name Value 10−1 C dC decicoulomb 101 C daC decacoulomb 10−2 C cC centicoulomb 102 C hC hectocoulomb 10−3 C mC millicoulomb 103 C kC kilocoulomb 10−6 C µC microcoulomb 106 C MC megacoulomb 10−9 C nC nanocoulomb 109 C GC gigacoulomb 10−12 C pC picocoulomb 1012 C TC teracoulomb 10−15 C fC femtocoulomb 1015 C PC petacoulomb 10−18 C aC attocoulomb 1018 C EC exacoulomb 10−21 C zC zeptocoulomb 1021 C ZC zettacoulomb 10−24 C yC yoctocoulomb 1024 C YC yottacoulomb

## Conversions

• The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022×1023, or Avogadro's number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals Script error: No such module "Gaps".. In terms of Avogadro's number (NA), one coulomb is equal to approximately 1.036 × NA×10−5 elementary charges.
• One ampere-hour = 3600 C, 1 mA⋅h = 3.6 C.
• The elementary charge is 1.602176565(35)×1019Lua error: Unmatched close-bracket at pattern character 67..[7]
• One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately 3.3356×1010 C or about one-third of a nanocoulomb.
• One coulomb is the magnitude (absolute value) of electrical charge in Script error: No such module "Gaps". protons or electrons.[1]

## Relation to elementary charge

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is approximately 1.602176565(35)×1019Lua error: Unmatched close-bracket at pattern character 67.[7]. In SI, the elementary charge in coulombs is an approximate value: no experiment can be infinitely accurate. However, in other unit systems, the elementary charge has an exact value by definition, and other charges are ultimately measured relative to the elementary charge.[8] For example, in conventional electrical units, the values of the Josephson constant KJ and von Klitzing constant RK are exact defined values (written KJ-90 and RK-90), and it follows that the elementary charge e = 2/(KJRK) is also an exact defined value in this unit system.[8] Specifically, e90 = (2×109)/(25812.807 × 483597.9) C exactly.[8] SI itself may someday change its definitions in a similar way.[8] For example, one possible proposed redefinition is "the ampere...is [defined] such that the value of the elementary charge e (charge on a proton) is exactly 1.602176487×1019Lua error: Unmatched close-bracket at pattern character 67.",[9] (in which the numeric value is the 2006 CODATA recommended value, since superseded). This proposal is not yet accepted as part of the SI; the SI definitions are unlikely to change until at least 2015.[10]

## In everyday terms

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.[11]
• The amount of charge that travels through a lightning bolt is typically around 15 C, although large bolts can be up to 350 C.[12]
• The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC = 5000 C ≈ 1400 mA⋅h.[13]
• According to Coulomb's law, two negative point charges of +1Lua error: Unmatched close-bracket at pattern character 67., placed one meter apart, would experience a repulsive force of 9×109Lua error: Unmatched close-bracket at pattern character 67., a force roughly equal to the weight of Script error: No such module "Gaps". metric tons of mass on the surface of the Earth.
• The hydraulic analogy uses everyday terms to illustrate movement of charge and the transfer of energy. The analogy equates charge to a volume of water, and voltage to pressure. One coulomb equals (the negative of) the charge of 6.24×1018Lua error: Unmatched close-bracket at pattern character 67.. The amount of energy transferred by the flow of 1 coulomb can vary; for example, 300 times fewer electrons flow through a lightning bolt than through an AA battery, but the total energy transferred by the flow of the lightning's electrons is 300 million times greater.

## Notes and references

1. ^ a b Script error: No such module "Gaps". is the reciprocal of the 2010 CODATA recommended value Script error: No such module "Gaps". for the elementary charge in coulomb.
2. ^ "SI Brochure, Appendix 1," (PDF). BIPM. p. 144.
3. ^ "SI brochure, section 2.2.2". BIPM.
4. ^
5. ^
6. ^ a b "Watt Balance". BIPM.
7. ^ a b c "CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2011. Retrieved 2011-06-23.
8. ^ a b c d Mills, I. M.; Mohr, P. J.; Quinn, T. J.; Taylor, B. N.; Williams, E. R. (2005). "Redefinition of the kilogram: a decision whose time has come". Metrologia 42 (2): 71. Bibcode:2005Metro..42...71M. doi:10.1088/0026-1394/42/2/001.
9. ^ Report of the CCU to the 23rd CGPM
10. ^ Anon (November 2010). "BIPM Bulletin" (PDF). BIPM. Retrieved 2011-01-28.
11. ^ Martin Karl W. Pohl. "Physics: Principles with Applications" (PDF). DESY.
12. ^ Hasbrouck, Richard. Mitigating Lightning Hazards, Science & Technology Review May 1996. Retrieved on 2009-04-26.
13. ^ How to do everything with digital photography – David Huss, p. 23, at Google Books, "The capacity range of an AA battery is typically from 1100–2200 mAh."