Coulomb

For other uses, see Coulomb (disambiguation).

coulomb
Unit system:	SI derived unit
Quantity:	Electric charge
Symbol:	C
Dimension:	T⋅I
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

The coulomb (unit symbol: C) is the SI derived unit of electric charge (symbol: Q or q). 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 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.

Definition

In the SI system, the coulomb is defined in terms of the ampere and second: 1C = 1A × 1s. The second is defined in terms of a frequency which is naturally emitted by caesium atoms. The ampere is defined using Ampère's force law; the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France. In practice, the watt balance is used to measure amperes with the highest possible accuracy.
Since the charge of one electron is known to be about 1.60217657 × 10^-19 coulombs, a coulomb can also be considered to be the charge of roughly 6.241509324 × 10¹⁸ electrons (or protons; electrons are technically represented with a charge in negative coulombs, and protons positive, but protons do not move in a circuit, electrons do; for electrical purposes charge is generally represented with an absolute value), though this is not standard practice, and does not define the unit in any official sense.^{[Note: citations needed, may be redundant]}

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	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

• 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 mA⋅h = 3.6 C
• The elementary charge is 1.602176487×10⁻¹⁹ C
• One statcoulomb (statC), the CGS electrostatic unit of charge (esu), is approximately 3.3356×10⁻¹⁰ C or about 1/3 nC. (other sources give 4.803E-10 esu /e-)
• One coulomb is the magnitude (absolute value) of electrical charge in 6.24150965(16)×10¹⁸ protons or electrons.

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. 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. 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. Specifically, $e_{90} = (2 \times 10^{-9})/(25812.807 \times 483597.9) C$ exactly. SI itself may someday change its definitions in a similar way. 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" This proposal is not yet accepted as part of the SI system: The SI definitions are unlikely to change until at least 2015.

In everyday terms

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.
• The amount of charge that travels through a lightning bolt is typically around 15 C, although large bolts can be up to 350 C.
• The amount of charge that travels through a typical alkaline AA battery is about 5 kC = 5000 C ≈ 1.4 A⋅h. After that charge has flowed, the battery must be discarded or recharged.
• 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 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