Coulomb

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For other uses, see Coulomb (disambiguation).
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    2997924580 statC
   Atomic units    6.24150965(16)e×10^18[1]

The coulomb (named after Charles-Augustin de Coulomb, unit symbol: C) is a fundamental unit of electrical charge, and is also the SI derived unit of electric charge (symbol: Q or q). It is equal to the charge of approximately 6.241×1018 electrons.

Its SI definition is the charge transported by a constant current of one ampere in one second:

1\ \mathrm{C} = 1\ \mathrm{A} \cdot 1\ \mathrm{s}

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

1\ \mathrm{C} = 1\ \mathrm{F} \cdot 1\ \mathrm{V}

Name and notation[edit]

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 capitalized material such as a title. 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[edit]

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 1.60217657×10^−19 coulombs,[1] a coulomb can also be considered to be the charge of roughly 6.241509324×10^18 electrons (or protons), the reciprocal of 1.60217657×10^−19.

SI prefixes[edit]

SI multiples for coulomb (C)
Submultiples Multiples
Value Symbol Name Value Symbol Name
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
Common multiples are in bold face.

See also SI prefix.

Conversions[edit]

Relation to elementary charge[edit]

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is approximately 1.602176487(40)×10^−19 C.[1] 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.[7] 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.[7] Specifically, e90 = (2×10−9)/(25812.807 × 483597.9) C exactly.[7] SI itself may someday change its definitions in a similar way.[7] 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 1.602176487×10^−19 coulombs"[8] This proposal is not yet accepted as part of the SI; the SI definitions are unlikely to change until at least 2015.[9]

In everyday terms[edit]

  • The charges in static electricity from rubbing materials together are typically a few microcoulombs.[10]
  • The amount of charge that travels through a lightning bolt is typically around 15 C, although large bolts can be up to 350 C.[11]
  • The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC = 5000 C ≈ 1.4 A⋅h.[12]
  • According to Coulomb's law, two negative point charges of 1 C, placed one meter apart, would experience a repulsive force of 9×109 N, a force roughly equal to the weight of 920000 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 6.24×1018 electrons. 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.

See also[edit]

Notes and references[edit]

  1. ^ a b c d e Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633.  Direct link to value. The inverse value (the number of elementary charges in 1 C) is given by 1/[1.602176487(40)×10^−19] = 6.24150965(16)×10^18.
  2. ^ "SI Brochure, Appendix 1,". BIPM. p. 144. 
  3. ^ "SI brochure, section 2.2.2". BIPM. 
  4. ^ "SI brochure, section 2.2.1.3". BIPM. 
  5. ^ "SI brochure, section 2.2.1.4". BIPM. 
  6. ^ a b "Watt Balance". BIPM. 
  7. ^ 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.  edit
  8. ^ Report of the CCU to the 23rd CGPM
  9. ^ Anon (November 2010). "BIPM Bulletin". BIPM. Retrieved 2011-01-28. 
  10. ^ Martin Karl W. Pohl. "Physics: Principles with Applications". DESY. 
  11. ^ Hasbrouck, Richard. Mitigating Lightning Hazards, Science & Technology Review May 1996. Retrieved on 2009-04-26.
  12. ^ 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."