Electromagnetism: Maxwell Equations, Wave Propagation and Emission

Chapter 6

Magnetic Field in Vacuum

The Earth’s magnetic field and the magnetism of some natural ores or iron rods that have been stroked by a magnet, have been known in the Middle East and China since antiquity. In 1821 Oersted discovered that an electric current produces a magnetic field. This effect was studied by Ampère, Biot, Savart, and others. Ampère assumed that permanent magnetism is due to microscopic currents in matter; this idea is retained in modern physics. Conversely, Faraday discovered in 1831 that a variable magnetic field induces an electric current in circuits. In 1888, Maxwell unified electricity and magnetism in a single theory, called electromagnetism. Currently, magnetism has many technological applications: magnets and electromagnets are used in generators and motors, instruments, computers, telecommunications, etc.

In this chapter, we introduce the concept of magnetic field and we study its action on magnetic currents. Then we study the creation of magnetic fields by moving charges and currents, magnetic energy and the interactions of circuits.

6.1. Force exerted by a magnetic field on a moving charge

The magnetic field is defined by its action on a charged particle in motion (Figure 6.1a in the case of positive charge). The experiment shows that this force is given by:

B is the magnetic field or, more precisely, the magnetic induction field. The magnetic ...