18.4 Coulomb’s law

Learning objectives

By the end of this section, you will be able to:

• State Coulomb's law in terms of how the electrostatic force changes with the distance between two objects.
• Calculate the electrostatic force between two point charges, such as electrons or protons.
• Compare the electrostatic force to the gravitational attraction for a proton and an electron; for a human and the Earth.

The information presented in this section supports the following AP® learning objectives and science practices:

• 3.A.3.3 The student is able to describe a force as an interaction between two objects and identify both objects for any force. (S.P. 1.4)
• 3.A.3.4 The student is able to make claims about the force on an object due to the presence of other objects with the same property: mass, electric charge. (S.P. 6.1, 6.4)
• 3.C.2.1 The student is able to use Coulomb's law qualitatively and quantitatively to make predictions about the interaction between two electric point charges (interactions between collections of electric point charges are not covered in Physics 1 and instead are restricted to Physics 2). (S.P. 2.2, 6.4)
• 3.C.2.2 The student is able to connect the concepts of gravitational force and electric force to compare similarities and differences between the forces. (S.P. 7.2)

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 $\left(F\propto 1/r^2\right)$ to an accuracy of 1 part in ${\text{10}}^{\text{16}}$ . No exceptions have ever been found, even at the small distances within the atom.