How did Coulomb study the repulsion and attraction forces of charged particles?
Coulomb thought of a following simple way, if there is q charge in a small metallic sphere and we touch it with another similar uncharged sphere, then by the symmetry, the charges on each of the spheres become q/2 due to redistribution.
Continuing the above step, he obtained charges q/4, q/8 etc.
Now he varied the distance between a fixed pair of charges and measured the force.
In the next step, he varied the charges in pairs and kept them at fixed separations.
He thus, finally arrived at the law that we call the Coulomb's law.
He did all this without knowing the explicit magnitude of the charge.
Amazing, isn't it ?
Oh, yes, I forgot to mention that he used a torsion balance to measure force.