How was Coulomb's law equation created?

is an empirical formula first published by Charles Augustin de Coulomb in the 18th century. The formula was based on experiments involving pith balls on a torsion balance. It describes the force between two point charges (charges that are small compared to the distance between them).

##\vec{F} = k_e \frac{ Q_1 Q_2}{r^2}\hat{r}##

where ##F## is the force of one charge on the other, ##Q_1## and ##Q_2## are the magnitudes of the two charges, ##r## is the distance between them, ##\hat{r}## is a unit vector pointing from one charge to the other. The quantity ##k_e = 9\times10^9 N\cdot m^2 C^{ -2}## is a constant of proportionality. The force attractive if the charges are of opposite kind, and repulsive if they are of like kind.

This formula says the force between the two charges is directly proportional to the charge of each body, inversely proportional to the square of the distance between them, and directed along the line joining their centers.

Coulomb first arrived at this formula by using a torsion balance to measure the force between two charged pith balls as a function of their separation. He used charging by induction to charge the pith balls in a repeatable, quantifiable way.

A torsion balance is a beam on the end of a vertical wire. The wire resists twisting in a predictable way, much like a Hooke's law spring, but it resists change in angle rather than in position. Coulomb placed pith balls on the ends of the beam, and brought other charged pith balls close to them to cause the beam to rotate.

The Gravitational constant "big G" was first measured by Cavendish using a very similar experimental setup to the one used by Coulomb to measure electrostatic forces.