Coulomb measured the force between two point charges and found that it varied inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges.
Thus, if two point charges q1, q2 are separated by a distance r in vacuum, the magnitude of the force (F) between them is given by
The choice of k determines the size of the unit of charge. In SI units, the value of k is about 9 × 109. Putting this value of k in above Equation, we see that for q1 = q2 = 1 C, r = 1 m F = 9 × 109 N
That is, 1 C is the charge that when placed at a distance of 1 m from another charge of the same magnitude in vacuum experiences an electrical force of repulsion of magnitude 9 × 109 N.
The constant k in is usually put as
for later convenience, so that Coulomb’s law is written as
The value of Permittivity of free space in SI units is equal to 8.854 × 10–12 C2 N–1m–2