3.1 INTRODUCTION

In this chapter, we shall recast the familiar force laws of electrostatics and magnetostatics as vector field equations.

3.2 COULOMB'S LAW

Between 1785 and 1787, the French physicist Charles Augustine de Coulomb performed a series of experiments involving electric charges, and eventually established what is nowadays known as Coulomb's law. According to this law, the force acting between two static electric charges is central, inverse-square, and proportional to the product of the charges. Two like charges repel one another, whereas two unlike charges attract. Suppose that two charges, q ₁ and q ₂, are located at position vectors r1 and r2, respectively. The electrical force acting on the second charge is written

in vector notation see Figure 3.1. An equal and opposite force acts on the first charge, in accordance with Newton's third law of motion. The SI unit of electric charge is the coulomb (C). The magnitude of the charge on an electron is 1.6022 lO ^?19 C. Finally, the universal constant ? ₀ is called the permittivity of free space, and takes the value

Figure 3.1: Coulomb's law.

Suppose that two masses, m ₁ and m ₂, are located at position vectors r ₁ and r ₂, respectively. According to Newton's law of gravity, the gravitational force acting on the second mass is written

in vector notation. The gravitational constant G takes the value

Note that Coulomb's law has the same mathematical form as...