**Coulomb's law** is a physical law stating the force between two charges is proportional to the amount of charge on both charges and inversely proportional to the square of the distance between them. The law is also known as Coulomb's inverse square law.

## Coulomb's Law Equation

The formula for Coulomb' law is used to express the force through which stationary charged particles attract or repel one another. The force is attractive if the charges attract each other (have opposite signs) or repulsive if the charges have like signs.

The scalar form of Coulomb's law is:

F = kQ_{1}Q_{2}/r^{2}

or

F ∝ Q_{1}Q_{2}/r^{2}

where

k = Coulomb's constant (9.0×10^{9} N m^{2} C^{−2}) F = force between the charges

Q^{1} and Q^{2} = amount of charge

r = distance between the two charges

A vector form of the equation is also available, which may be used to indicate both the magnitude and direction of the force between the two charges.

There are three requirements which must be met in order to use Coulomb's law:

- The charges must be stationary with respect to each other.
- The charges must be non-overlapping.
- The charges must be either point charges or else otherwise spherically symmetrical in shape.

## History

Ancient people were aware certain objects could attract or repel each other. At the time, the nature of electricity and magnetism was not understood, so the underlying principle behind magnetic attraction/repulsion versus the attraction between an amber rod and fur was thought to be the same. Scientists in the 18th century suspected the force of the attraction or repulsion diminished based on the distance between two objects. Coulomb's law was published by French physicist Charles-Augustin de Coulomb in 1785. It may be used to derive Gauss's law. The law is considered to be analogous to Newton's inverse square law of gravity.

## Sources

- Baigrie, Brian (2007).
*Electricity and Magnetism: A Historical Perspective*. Greenwood Press. pp. 7–8. ISBN 978-0-313-33358-3 - Huray, Paul G. (2010).
*Maxwell's Equations*. Wiley. Hoboken, NJ. ISBN 0470542764. - Stewart, Joseph (2001).
*Intermediate Electromagnetic Theory*. World Scientific. p. 50. ISBN 978-981-02-4471-2