Introduction

Two Things We Already Know

By this point in the course, two results are already familiar:

1. A steady electric current produces a magnetic field, and two current-carrying wires exert a magnetic force on each other (Chapter 4).
2. A magnetic field that changes with time gives rise to an electric field — this is Faraday's law (Chapter 6).

The Question Maxwell Asked

Is the converse also true — does an electric field that changes with time give rise to a magnetic field? James Clerk Maxwell (1831–1879) argued that it does: not just a conduction current, but also a time-varying electric field, generates a magnetic field.

Maxwell arrived at this while applying Ampere's circuital law to find the magnetic field at a point outside a capacitor being charged by a time-varying current — he noticed the law gave an inconsistent (contradictory) answer depending on how it was applied. To remove this inconsistency, he proposed the existence of an additional current, which he called the displacement current. (The details of this argument and how the displacement current is defined are worked out in the next section.)

Maxwell's Equations

Maxwell combined this idea with the existing laws of electricity and magnetism into a set of four equations relating the electric and magnetic fields to their sources — the charge and current densities. These are known as Maxwell's equations. Together with the Lorentz force law (Chapter 4), they express, in mathematical form, all of the basic laws of electromagnetism.

The Big Prediction: Electromagnetic Waves

The most important consequence of Maxwell's equations is the prediction that electromagnetic waves exist — coupled, time-varying electric and magnetic fields that propagate through space, regenerating each other as they travel. Maxwell calculated the speed such a wave should have from his equations, and found it came out very close to the speed of light (3 × 10⁸ m/s) already measured by optical experiments. This was a striking result: it meant light itself is an electromagnetic wave, unifying the previously separate subjects of electricity, magnetism, and optics into one theory.

The prediction did not stay purely theoretical for long. In 1885, Heinrich Hertz experimentally generated and detected electromagnetic waves in the laboratory, confirming Maxwell's theory directly. The technological exploitation of this discovery — by Marconi and others — went on to spark the revolution in long-distance communication that continues today.

What This Chapter Covers

This chapter first develops the need for the displacement current and works out its consequences (§8.2). It then gives a descriptive account of electromagnetic waves themselves — how they are produced, their key properties, and how they carry energy. Finally, it surveys the broad electromagnetic spectrum, which stretches all the way from gamma rays (wavelength ~10⁻¹² m) to long radio waves (wavelength ~10⁶ m).