Coulomb

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The coulomb (symbol: C) is the SI unit of electric charge. It is named after Charles-Augustin de Coulomb.

1 Definition
2 Explanation
3 Historical note
4 SI multiples
5 Conversions
6 See also

Definition

1 coulomb is the amount of electric charge carried by a current of 1 ampere flowing for 1 second.

<math> 1 \,\mathrm{C} = 1 \,\mathrm{A} \cdot 1 \,\mathrm{s}</math>

It can also be defined in terms of capacitance and voltage, where one coulomb is defined as one farad of capacitance times one volt of electric potential difference:

<math>1 \,\mathrm{C} = 1 \,\mathrm{F} \cdot 1 \,\mathrm{V}</math>

Explanation

The coulomb is also the unit of electric flux. (See Gauss Law.)

In principle, the coulomb could be defined in terms of the charge of an electron or elementary charge. Since the values of the Josephson (CIPM (1988) Recommendation 1, PV 56; 19) and von Klitzing (CIPM (1988), Recommendation 2, PV 56; 20) constants have been given conventional values (K_J ≡ 4.835 979×10¹⁴ Hz/V and R_K ≡ 2.581 280 7×10⁴ Ω), it is possible to combine these values to form an alternative (not yet official) definition of the coulomb. A coulomb is then equal to exactly 6.241 509 629 152 65×10¹⁸ elementary charges. Combined with the current definition of the ampere, this proposed definition would make the kilogram a derived unit.

If two point charges of + 1 C are held one meter away from each other, the repulsive force they will feel is given by Coulomb's Law as 8.988×10⁹ N [1]. This is roughly equal to the gravitational force of 900,000 metric tons of mass at the surface of the Earth. Because these forces are so large, it can be informally stated that "a coulomb is a lot of charge." In everyday life, most things don't have a large surplus of charge -- e.g. normal human beings standing one meter away from each other generally don't feel any electrostatic force between them, and have a capacity to feel a force of ~10 N (~1 kg). From this, it can be conjectured that they generally have a net charge of less than 30 µC [2].

Historical note

The ampere was historically a derived unit - being defined as 1 coulomb per second. Therefore the coulomb, rather than the ampere, was the SI base electrical unit.

In 1960 the SI system made the ampere the base unit (See http://alpha.montclair.edu/~kowalskiL/SI/SI_PAGE.HTML).

SI multiples

Multiple	Name	Symbol	Multiple	Name	Symbol
10⁰	coulomb	C
10¹	decacoulomb	daC	10^–1	decicoulomb	dC
10²	hectocoulomb	hC	10^–2	centicoulomb	cC
10³	kilocoulomb	kC	10^–3	millicoulomb	mC
10⁶	megacoulomb	MC	10^–6	microcoulomb	µC
10⁹	gigacoulomb	GC	10^–9	nanocoulomb	nC
10¹²	teracoulomb	TC	10^–12	picocoulomb	pC
10¹⁵	petacoulomb	PC	10^–15	femtocoulomb	fC
10¹⁸	exacoulomb	EC	10^–18	attocoulomb	aC
10²¹	zettacoulomb	ZC	10^–21	zeptocoulomb	zC
10²⁴	yottacoulomb	YC	10^–24	yoctocoulomb	yC

Conversions

The electrical charge of one mole of electrons (approximately 6.022×10²³, or Avogadro's number) is known as a faraday (actually -1 faraday, since electrons are negatively charged). One faraday equals 96.485 341 5 kC (the Faraday constant). 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

The elementary charge is approximately 160.2176 zC.

One statcoulomb (statC), the CGS electrostatic unit of charge (esu), is approximately 3.3356×10^-10 C or about 1/3 nC.

1 coulomb is the amount of electrical charge in 6.241506×10¹⁸ electrons or other elementary charged particles.

The charge of one electron is equal to -1.6022×10^-19 C

Image:SI Brochure Cover.jpg

This SI unit is named after Charles-Augustin de Coulomb. As for all SI units whose names are derived from the proper name of a person, the first letter of its symbol is uppercase (C). But when an SI unit is spelled out, it should always be written in lowercase (coulomb), unless it begins a sentence or is the name "degree Celsius".

— Based on The International System of Units, section 5.2.