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How did Coulomb find the law of value of...

How did Coulomb find the law of value of electric force between two point charges ?

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`rArr` Coulomb supposed the charge on a metallic sphere is q. If the sphere is put in contact with an identical uncharged sphere, the charge wil! spread over the two spheres. By symmetry the charge on each sphere will be `q/2`.
`rArr` Repeating this process we can get charges `q/2` and `q/4` etc.
`rArr` pheres are obtained with pairs of electric charges of `q/2, q/4, q/8`,.............. by repeating this proccs.
Coulomb varied the distance for a fixed pair of charges and measured the force for different separations. Then he gave relation `F prop 1/r^(2)`.......(1)
He then varied the charges in pairs, keeping the distance fixed for each pair. Comparing forces. for different pairs of charges at different distances, Coulomb gave the relation.
`F prop q_(1)q_(2)`.........(2)
Thus, the electric force between two electric charges, `F prop (q_(1)q_(2))/r^(2)`
`therefore F = k.(q_(1)q_(2))/r^(2)`, where k is coulombian constant.
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