# Electric Charge and Electric Field

## Coulomb’s Law


### Learning Objectives

By the end of this section, you will be able to:
1. State Coulomb’s law in terms of how the electrostatic force changes with the distance between two objects.
2. Calculate the electrostatic force between two charged point forces, such as electrons or protons.
3. Compare the electrostatic force to the gravitational attraction for a proton and an electron; for a human and the Earth.
Through the work of scientists in the late 18th century, the main features of the electrostatic force—the existence of two types of charge, the observation that like charges repel, unlike charges attract, and the decrease of force with distance—were eventually refined, and expressed as a mathematical formula. The mathematical formula for the electrostatic force is called Coulomb’s law after the French physicist Charles Coulomb (1736–1806), who performed experiments and first proposed a formula to calculate it.
Although the formula for Coulomb’s law is simple, it was no mean task to prove it. The experiments Coulomb did, with the primitive equipment then available, were difficult. Modern experiments have verified Coulomb’s law to great precision. For example, it has been shown that the force is inversely proportional to distance between two objects squared  to an accuracy of 1 part in . No exceptions have ever been found, even at the small distances within the atom.

As the example implies, gravitational force is completely negligible on a small scale, where the interactions of individual charged particles are important. On a large scale, such as between the Earth and a person, the reverse is true. Most objects are nearly electrically neutral, and so attractive and repulsive Coulomb forces nearly cancel. Gravitational force on a large scale dominates interactions between large objects because it is always attractive, while Coulomb forces tend to cancel.

### Test Prep for AP Courses


### Section Summary

1. Frenchman Charles Coulomb was the first to publish the mathematical equation that describes the electrostatic force between two objects.
2. Coulomb’s law gives the magnitude of the force between point charges. It is
                where 
3. This Coulomb force is extremely basic, since most charges are due to point-like particles. It is responsible for all electrostatic effects and underlies most macroscopic forces.
4. The Coulomb force is extraordinarily strong compared with the gravitational force, another basic force—but unlike gravitational force it can cancel, since it can be either attractive or repulsive.
5. The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles.

### Conceptual Questions


### Problems & Exercises
