Coulomb's Law of Electrostatics/SI Units

Physical Law
Coulomb's Law of Electrostatics gives the force between two stationary charged particles $a$ and $b$ as:


 * $\mathbf F_{a b} \propto \dfrac {q_a q_b {\mathbf r_{a b} } } {r^3}$

where:
 * $q_a$ and $q_b$ are the charges on $a$ and $b$ respectively
 * $\mathbf F_{a b}$ is the force exerted on $b$ by the electric charge on $a$
 * $\mathbf r_{a b}$ is the displacement vector from $a$ to $b$
 * $r$ is the distance between $a$ and $b$.
 * the constant of proportion is defined as being positive.

In SI units, the law becomes:
 * $\mathbf F_{a b} = \dfrac 1 {4 \pi \varepsilon_0} \dfrac {q_a q_b {\mathbf r_{a b} } } {r^3}$

where:
 * $q_a$ and $q_b$ are measured in coulombs
 * $r$ is measured in metres
 * $F_{a b}$ is measured in newtons
 * $\varepsilon_0$ denotes the vacuum permittivity:
 * $\varepsilon_0 \approx 8 \cdotp 85418 \, 78128 (13) \times 10^{-12} \, \mathrm C^2 \, \mathrm N^{-1} \, \mathrm m^{-2}$