Introduction and Definition:
The force between two particles was studied by Coulomb in 1785. He stated that the force of attraction or repulsion between two charged particles is directly proportional to the product of the charges and indirectly proportional to the square of the distance between them. The direction of force is along the straight line joining them.
Derivation:
Suppose q1 and q2 are the two point charges which are being separated by a distance of r units apart, then according to coulomb’s law F α q_{1}q_{2}/r^{2} or F = k q_{1}q_{2}/r^{2} where k is the constant of proportionality. In air or vacuum the value of k is 1/4∏€_{0} where €_{0} the permittivity of free space is. Its value is given by 8.854 x 10^{-12 }C²N-^{1}m^{-2}.
Hence F =1/4∏€_{0} X q_{1}q_{2}/r^{2} -------------------------à(1)
Definition for Coulomb:
One Coulomb is defined as the quantity of charge, which when placed at a distance of 1 metre in air or vacuum from an equal and similar charge, experiences a repulsive force of 9 x 10^{9} Nm²C^{-2}