Coulomb measured the force of attraction and repulsion between two stationary charges by using a torsion balance. His observations are known as Coulomb’s law.
Coulomb’s Law states that:
Stationary charges attract or repel each other with a force which is directly proportional to the product of magnitude of the charges and inversely proportional to the square of the distance between them.
Suppose there are two charges $q_1$ and $q_2$ which are $r$ distance apart.
Then, according to Coulomb’s law,
\[F∝q_1q_2\]
and, \[F∝\frac{1}{r^2}\]
Combining above two equations, we get,
\[F∝\frac{q_1q_2}{r^2}\] \[\text{or, }F=k \frac{q_1q_2}{r^2}\]
where, $k$ is proportionality constant.
The value of $k$ depends upon;
1. The medium in which the two charges are present.
2. The system of units in which $F$, $q$, and $r$ are measured.
If the charges are located in air or vacuum, then,
\[k=\frac{1}{4πε_0}\]
where, $ε_0$ is known as permitivity of free space. Its unit is $\text{Coulomb}^2 \text{Newton}^{-1} \text{metre}^{-2}$ $(\text{C}^2\text{N}^{-1}\text{m}^{-2})$. Its value is found to be $8.854 × 10^{-12}$ $\text{C}^2\text{N}^{-1}\text{m}^{-2}$.
\[∴ F=\frac{1}{4πε_0}\cdot \frac{q_1q_2}{r^2}\]
More on Electric Field