Coulomb

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)×1018 e[1]

The coulomb (symbol: C) is the SI derived unit of electric charge. It is defined as the charge transported by a steady current of one ampere in one second:

$1 \mathrm{C} = 1 \mathrm{A} \times 1 \mathrm{s}$

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

$1 \mathrm{C} = 1 \mathrm{F} \times 1 \mathrm{V}$

Name and notation

This SI unit is named after Charles-Augustin de Coulomb. As with every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (C). When an SI unit is spelled out in English, it should always begin with a lower case letter (coulomb), except where any word 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

In the SI system, the coulomb is defined in terms of the ampere and second: 1C = 1A × 1s.^[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]

SI prefixes

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	not used		1021 C	ZC	zettacoulomb
10−24 C	yC	not used		1024 C	YC	yottacoulomb
Common multiples are in bold face.

See also SI prefix.

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 is equal to 96485.3399 coulombs. In terms of Avogadro's number (N_A), one coulomb is equal to approximately 1.036 × N_A ×10⁻⁵ elementary charges.
• one ampere-hour = 3600 C, 1 mAh = 3.6 C
• The elementary charge is 1.602176487×10⁻¹⁹ C^[1]
• One statcoulomb (statC), the CGS electrostatic unit of charge (esu), is approximately 3.3356×10⁻¹⁰ C or about 1/3 nC.
• One coulomb is the magnitude (absolute value) of electrical charge in 6.24150965(16)×10¹⁸ 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 1.602176487(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 K_J and von Klitzing constant R_K are exact defined values (written K_J-90 and R_K-90), and it follows that the elementary charge e = 2 / (K_JR_K) is also an exact defined value in this unit system.^[7] Specifically, $e_{90} = (2 \times 10^{-9})/(25812.807 \times 483597.9) C$ 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 coulomb"^[8] This proposal is not yet accepted as part of the SI system: The SI definitions are unlikely to change until at least 2015.^[9]

In everyday terms

• 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 is about 5 kC = 5000 C = 1400 mAh. After that charge has flowed, the battery must be discarded or recharged.^[12]
• According to Coulomb's Law, two 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 920,000 metric tons of mass on the surface of the Earth.

See also

• Abcoulomb, a cgs unit of charge
• Ampère's circuital law
• Coulomb's law
• Electrostatics
• Elementary charge
• Faraday (unit), an obsolete unit
• Quantity of electricity

References

1. ^ ^{a b c d} Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80: 633–730. Bibcode 2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. http://physics.nist.gov/cuu/Constants/codata.pdf.  Direct link to value. The inverse value (the number of elementary charges in 1C) is given by 1/[1.602176487(40)×10^-19] = 6.24150965(16)×10¹⁸.
2. ^ "SI Brochure, Appendix 1,". BIPM. p. 144. http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf. 
3. ^ "SI brochure, section 2.2.2". BIPM. http://www.bipm.org/en/si/si_brochure/chapter2/2-2/table3.html. 
4. ^ "SI brochure, section 2.2.1.3". BIPM. http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html. 
5. ^ "SI brochure, section 2.2.1.4". BIPM. http://www.bipm.org/en/si/si_brochure/chapter2/2-1/ampere.html. 
6. ^ ^{a b} "Watt Balance". BIPM. http://www.bipm.org/en/scientific/elec/watt_balance/. 
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: 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. http://www.bipm.org/utils/en/pdf/BIPM_Bulletin.pdf. Retrieved 2011-01-28. 
10. ^ Martin Karl W. Pohl. "Physics: Principles with Applications". DESY. http://www-zeuthen.desy.de/~pohlmadq/teach/112/ch16.pdf. 
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 at Google Books, "The capacity range of an AA battery is typically from 1100–2200 mAh."