Charles Coulomb (1736–1806) measured the magnitudes of the electric forces between
charged objects using the torsion balance, which he invented (Fig. 23.6). Coulomb con-
firmed that the electric force between two small charged spheres is proportional to the
inverse square of their separation distance r—that is, Fe % 1/r 2. The operating principle
of the torsion balance is the same as that of the apparatus used by Cavendish to measure
the gravitational constant (see Section 13.2), with the electrically neutral spheres
replaced by charged ones. The electric force between charged spheres A and B in Figure
23.6 causes the spheres to either attract or repel each other, and the resulting motion
causes the suspended fiber to twist. Because the restoring torque of the twisted fiber is
proportional to the angle through which the fiber rotates, a measurement of this angle
provides a quantitative measure of the electric force of attraction or repulsion. Once the
spheres are charged by rubbing, the electric force between them is very large compared
with the gravitational attraction, and so the gravitational force can be neglected.
From Coulomb’s experiments, we can generalize the following properties of the
electric force between two stationary charged particles. The electric force