Magnitude of Electric forces between the charged objects was observed by the coulomb by using the torsion balance. We can directly come to the law but first we will discuss that how the coulomb law was derived by coulomb using the Torsion Balance.
Torsion balance was used by the coulomb for measuring the electrostatic force. Torsion balance is shown in the figure 1 below. There are two pith balls present in the torsion balance. One ball is mounted and present on the end of a glass rod. This ball is shown in red color and is unmovable. The other ball is shown in blue color. Blue ball can spin around and can move. Electrostatic Charge was given to both the balls. We can give electrostatic charge to the balls firstly by rubbing the rod of plastic with fur and then touching the plastic rod with the balls. Now what happened was, when similar type of charge was given to both the red and blue balls, the blue ball moved away from the red ball. But on the other hand, when different electrostatic charges were given to the red and blue balls, blue ball which is movable start moving towards the red ball which is unmovable. This shows that when both the balls were given same charge they repel each other but on the other hand when they were give different kind of charges they attracted each other. Electrostatic force between the balls was measured with the help of distance moved by the blue ball. Coulomb measured the torsion on the fiber with the help of scale near the top of the device and the distance between the two balls on the scale wrapped around the base of the jar. Mathematical equation was derived by him which showed the relationship between these two measurements.
He suggested and observed that the force between the charged objects or charged balls was inversely proportional to the distance between the balls and was directly proportional to the magnitude of charge on the balls.