Coulomb

The coulomb (symbol: C) is the SI unit of electric charge. It is named after Charles-Augustin de Coulomb (1736 to 1806).

Definition

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

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

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:

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

Explanation

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

The coulomb could in principle 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 Hz/V and R_K ≡ 2.581 280 7 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 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 N 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 [http://www.google.com/search?q=sqrt%2810+N+*++%284+*+pi+*+electric+constant+*+1+m%5E2%29%29. Yet everyday solid matter is composed of charged particles with an approximate density of several hundred coulombs per cubic millimeter, so we could also state that a coulomb is physically very small.

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,

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

SI multiples

Conversions

The electrical charge of one mole of electrons (approximately 6.022, 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 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 C or about 1/3 nC.

1 coulomb is the amount of electrical charge in 6.241 electrons or other elementary charged particles.

The charge of one electron is equal to 1.6022 C

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Definition

Explanation

Historical note

SI multiples

Conversions

See also