5 Let there be light!
5.1 Electromagnetic waves
This section gives a brief introduction to light and electromagnetic waves.
The idea that light is an electromagnetic wave had occurred to Faraday while Maxwell was still a schoolboy, but Maxwell was the first person to possess a complete set of equations describing the dynamical behaviour of electric and magnetic fields. Believing that Faraday was correct, Maxwell set out to show that his equations have wave-like solutions that propagate through empty space at the speed of light.
Electric and magnetic fields are produced by charges and currents, but these fields also extend into surrounding regions of empty space. For example, charges and currents in the Sun produce electromagnetic fields which travel across almost empty space before reaching sunbathers on a beach on Earth. The detailed relationship between the fields and their sources will not be discussed here. Instead, we take the existence of time-varying electric and magnetic fields for granted, and concentrate on their propagation through space. In empty space, the charge and current densities are equal to zero, so Maxwell's equations become
Our aim is to show that these equations have wave-like solutions which describe oscillating electric and magnetic fields that propagate through space. These wave-like solutions are called electromagnetic waves.