How did Coulomb discover Coulomb's law?

Answer 1

Charles-Augustin de Coulomb made use of the experimentation of Robert Hooke and his discovery of Hooke's Law in order to derive Coulomb's Law. In 1777, Coulomb invented and made use of the torsion balance, or the torsion pendulum, to measure electrostatic forces. The torsion balance is made from a bar suspended from its center by a thin fiber, which acts as a very weak torsion spring (torsion meaning twisting; as a torsion spring is twisted, it stores mechanical energy in likeness to a linear spring in the form of torque). When a force is applied to the bar at a right angle, it twists the torsion spring until equilibrium is reached, or when the force exerted by the spring is equal to the force exerted on the spring; at this point, the bar stops rotating. The angle at which the bar rests at equilibrium, in radians relative to its initial angular position, is proportional to the force applied on the spring by an angular variation of Hooke's Law, t = -kA, where t is torque, or force applied at a distance from a fulcrum, A is the angle, and k is a calculable constant specific to the spring. Coulomb used an insulating rod with a metal-coated ball attached to one end. The ball was charged with a known charge of static, and another charged ball of the same polarity was brought near. The two balls repelled each other, twisting the torsion spring until equilibrium. He compiled data using different charges and separations to derive the inverse square law, F = Kc|q1*q2|/(r2), using integral calculus. From experimental data, the constant Kc (Coulomb's constant) could be calculated as well. Repeated experimentation eventually established this relationship as a physical law.