Coulomb's constant

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:

Coulomb's law:

$|\boldsymbol{F}|=k_e{|q_1q_2|\over r^2}$.

Electric potential energy:

$U_E(r) = k_e\frac{qQ}{r}$.

Electric field:

$\mathbf{E} = k_e \sum_{i=1}^N \frac{Q_i}{r_i^2} \mathbf{\hat{r}}_i$.