# Coulomb's constant

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Coulomb's constant, the electric force constant, or the electrostatic constant (denoted k e ) is a proportionality constant in equations relating electric variables and is exactly equal to k e  = 8.9875517873681764×109 N·m2/C2 (m/F). It was named after the French physicist Charles-Augustin de Coulomb (1736–1806).

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## Use of Coulomb's constant

Coulomb's constant is used in many electric equations, although it is sometimes expressed as:

\begin{align} k_e &= \frac{1}{4\pi\varepsilon_0} \end{align}.

Some examples of use of Coulomb's constant are the following:

$|\boldsymbol{F}|=k_e{|q_1q_2|\over r^2}$.
$U_E(r) = k_e\frac{qQ}{r}$.
$\mathbf{E} = k_e \sum_{i=1}^N \frac{Q_i}{r_i^2} \mathbf{\hat{r}}_i$.