The first three sections have established a model of charges and electric forces. This model has successfully provided a qualitative explanation of electric phenomena; now it’s time to become quantitative. Experiment 4 in Section 22.1 found that the electric force decreases with distance. The force law that describes this behavior is known as Coulomb’s law.

Charles Coulomb was one of many scientists investigating electricity in the late 18th century. Coulomb had the idea of studying electric forces using the torsion balance scheme by which Cavendish had measured the value of the gravitational constant $G$ (see Section 13.4). This was a difficult experiment. Despite many obstacles, Coulomb announced in 1785 that the electric force obeys an inverse-square law analogous to Newton’s law of gravity. Today we know it as Coulomb’s law.

We sometimes speak of the “force between charge $q_1$ and charge $q_2$,” but keep in mind that we are really dealing with charged objects that also have a mass, a size, and other properties. Charge is not some disembodied entity that exists apart from matter. Coulomb’s law describes the force between charged particles, which are also called point charges. A charged particle, which is an extension of the particle model we used in Part I, has a mass and a charge but has no size.

Coulomb’s law looks much like Newton’s law of gravity, but there is one important difference: The charge $q$ can be either positive or negative. Consequently, the absolute value signs in Equation 22.2 are especially important. The first part of Coulomb’s law gives only the magnitude of the force, which is always positive. The direction must be determined from the second part of the law. FIGURE 22.15 shows the forces between different combinations of positive and negative charges.

FIGURE 22.15 Attractive and repulsive forces between charged particles.