# Law of Coulomb (electrostatic)

In electrostatic, the law of Coulomb expresses the electric force $\ vec \left\{F\right\} _ \left\{1 \ rightarrow 2\right\} \,$ exerted by a electric Charge $q_1 \,$ placed in a point $M_1 \,$ on a load $q_2 \,$ placed in a point $M_2 \,$. This law is expressed in vectorial form by the following formula:

$\ vec \left\{F\right\} _ \left\{1 \ rightarrow 2\right\} = \ frac \left\{q_1 q_2\right\} \left\{4 \ pi \ epsilon_0 \left\{\|\ vec \left\{R\right\} _ \left\{12\right\} \|\right\} ^2\right\}. \ frac \left\{\ vec \left\{R\right\} _ \left\{12\right\}\right\} \left\{\|\ vec \left\{R\right\} _ \left\{12\right\} \|\right\}$
where
• ε 0=8,854·10-12 F·m-1 is a universal constant called electric permittivity of the vacuum, and
• $\ vec \left\{R\right\} _ \left\{12\right\} = \ overrightarrow \left\{M_1M_2\right\}$ is the Vecteur position which connects the first body to the second.

In the system of units C.G.S. the law is written more simply

$\ vec \left\{F\right\} _ \left\{1 \ rightarrow2\right\} = \ frac \left\{q_1q_2\right\} \left\{\|\ vec \left\{R\right\} _ \left\{12\right\} \|^3\right\} \left\{\ vec \left\{R\right\} _ \left\{12\right\}\right\} \,$

with the lengths this time expressed in centimetres (cm) and them loads in electrostatic unit (esu).

NB: the law is not valid for loads moving but only in one reference frame where they are fixed.

## See too

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