Coulomb's law

Coulomb's law, sometimes called the Coulomb law, is an equation describing the electrostatic force between electric charges. It was studied and first published in the 1780s by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. Nevertheless, the dependence of the electric force with distance (inverse square law) had been proposed previously by Joseph Priestley and the dependence with both distance and charge had been discovered, but not published, by Henry Cavendish, prior to Coulomb's works.
Scalar form:-
The scalar form of Coulomb's law will only describe the magnitude of the electrostatic force between two electric charges. If direction is required, then the vector form is required as well. The magnitude of the electrostatic force (F) on a charge (q1) due to the presence of a second charge (q2), is given by
where r is the distance between the two charges and ke a proportionality constant. A positive force implies a repulsive interaction, while a negative force implies an attractive interaction.
The proportionality constant ke, called Coulomb's constant (sometimes called Coulomb's force constant) is related to the properties of space and can be calculated exactly:
In SI units the speed of light in vacuum, denoted c0[4] is defined as 299,792,458 m·s−1, and the magnetic constant (μ0), is defined as 4π × 10−7 H·m−1,[6] leading to the definition for the electric constant (ε0) as ε0 = 1/(μ0c20) ≈ 8.854187817×10−12 F·m−1. In cgs units, the unit charge, esu of charge or statcoulomb, is defined so that this Coulomb force constant is 1.
This formula says that the magnitude of the force is directly proportional to the magnitude of the charges of each object and inversely proportional to the square of the distance between them. The exponent in Coulomb's Law has been found to differ from −2 by less than one in a billion.
When measured in units that people commonly use (such as SI—see International System of Units), the electrostatic force constant (ke) is numerically much much larger than the universal gravitational constant (G).This means that for objects with charge that is of the order of a unit charge (C) and mass of the order of a unit mass (kg), the electrostatic forces will be so much larger than the gravitational forces that the latter force can be ignored. This is not the case when Planck units are used and both charge and mass are of the order of the unit charge and unit mass. However, charged elementary particles have mass that is far less than the Planck mass while their charge is about the Planck charge so that, again, gravitational forces can be ignored. For example, the electrostatic force between an electron and a proton, which constitute a hydrogen atom, is almost 40 orders of magnitude greater than the gravitational force between them.
Coulomb's law can also be interpreted in terms of atomic units with the force expressed in Hartrees per Bohr radius, the charge in terms of the elementary charge, and the distances in terms of the Bohr radius.