III. Observation experiment: How does electric force depend on the distance and the magnitude of charges (quantitative)? Charles Coulomb used the apparatus shown on the right to measure the force that one charged metal ball exerts on another charged ball. The magnitude of the force can be inferred from the angle at which the string twists when a charged object approaches a charged ball of the apparatus. Coulomb's goal was to find how the force between two electrically charged objects depends on the magnitudes of the charges and on their separation. At Coulomb's times people could not measure the absolute magnitude of the electric charge on the metal balls but they knew from observations that if you touch a charged metal ball with an identical uncharged metal ball, both will have the same charge equal to half of the original. Thus Coulomb could divide the charge on metal balls in half and he could also measure the magnitude of the force that the balls exerted on each other. The table below provides data that resembles what Coulomb might have collected. Find patterns in the data and devise a mathematical relationship involving the important physical quantities. Remember to decide which are the independent variables and which is the dependent variable. Then observe the dependent variable as you change only one independent variable at a time.