By the middle of the nineteenth century, scientists had discovered many important laws describing electricity and magnetism. Coulomb had explained electric forces, Gauss had described electric fields, Ørsted had shown that electric currents produce magnetic fields, Ampère had developed the mathematical description of those magnetic fields, and Faraday had discovered electromagnetic induction. Although these discoveries were individually important, they appeared to be separate pieces of a much larger puzzle.

Scottish physicist James Clerk Maxwell (1831–1879) assembled these seemingly independent ideas into a single, unified theory of electromagnetism. His work showed that electricity and magnetism are not separate phenomena but different aspects of the same fundamental interaction: the electromagnetic force. Even more remarkably, Maxwell's theory predicted the existence of electromagnetic waves years before they were observed experimentally.

Maxwell's theory is summarized by four equations known collectively as Maxwell's equations. Their full mathematical form requires advanced calculus and is beyond the scope of this course. Fortunately, their physical meaning can be understood with the concepts you have already learned.

Together, these four statements summarize nearly all of classical electricity and magnetism. Perhaps the most important insight was Maxwell's recognition that changing electric fields create magnetic fields, just as changing magnetic fields create electric fields. This symmetry allows electric and magnetic fields to continually regenerate one another, enabling electromagnetic waves to travel through empty space.

At the time Maxwell proposed his theory, the magnetic fields produced by changing electric fields were far too weak to detect directly. However, he realized that rapidly oscillating electric charges, such as those in alternating-current (AC) circuits, continually produce changing electric fields. According to his equations, these changing electric and magnetic fields should sustain one another and propagate through space as a wave.

Maxwell therefore predicted the existence of electromagnetic waves—waves consisting of oscillating electric and magnetic fields that travel without requiring a material medium. His theory showed that the speed of these waves should be

Substituting the known values of the permeability of free space, [latex]\mu_0[/latex], and the permittivity of free space, [latex]\epsilon_0[/latex], gives

This value is exactly the measured speed of light. Maxwell immediately recognized the significance of this result: visible light is an electromagnetic wave. If visible light is electromagnetic radiation, then many other wavelengths should also exist. Today we know that radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays are all members of the same electromagnetic spectrum.

Maxwell did not live to see his prediction confirmed. A few years after his death, Heinrich Hertz successfully generated and detected radio waves in the laboratory, providing spectacular experimental confirmation of Maxwell's theory. The following section describes Hertz's groundbreaking experiments and their lasting impact on science and technology.

Hertz's Experimental Confirmation

Although Maxwell's theory predicted the existence of electromagnetic waves, a prediction alone was not enough. The scientific community needed experimental evidence. That evidence came from the German physicist Heinrich Hertz (1857–1894), who became the first person to generate and detect electromagnetic waves in the laboratory. Beginning in 1887, Hertz carried out a series of elegant experiments that confirmed Maxwell's predictions and demonstrated that electromagnetic waves travel at the speed of light.

Hertz generated electromagnetic waves using a resonant RLC (resistor–inductor–capacitor) circuit connected to a loop of wire, as shown in Figure 59.2. The circuit oscillated at its resonant frequency,

[latex]f_0=\frac{1}{2\pi\sqrt{LC}}[/latex]

causing a rapidly changing current to flow through the wire. A small gap in the loop allowed high voltages to produce visible sparks. These rapidly oscillating currents generated electromagnetic waves that propagated outward through space.

Several meters away, Hertz placed a second wire loop connected to another resonant RLC circuit tuned to the same frequency. When the electromagnetic waves reached this second loop, they induced a current large enough to produce tiny sparks across its gap. These sparks demonstrated that energy had traveled through empty space without any physical connection between the two circuits.

Hertz did more than simply detect the waves. He demonstrated that they could be reflected, refracted, polarized, and interfere with one another—the same behaviors exhibited by visible light. By measuring their wavelength and combining it with the known oscillation frequency, he calculated their speed using

[latex]v=f\lambda[/latex]

where v is the wave speed, f is the frequency, and [latex]\lambda[/latex] is the wavelength. His measured value agreed with the speed of light, providing compelling evidence that visible light and radio waves are different forms of the same electromagnetic phenomenon.

Hertz viewed his work primarily as a confirmation of Maxwell's theory and did not anticipate its enormous practical impact. Within a few decades, however, his experiments became the scientific foundation for radio communication, television, radar, satellite communications, Wi-Fi, Bluetooth, cellular networks, and many medical technologies that rely on electromagnetic waves. In recognition of his contributions, the SI unit of frequency is named the hertz (Hz), where

[latex]1~\mathrm{Hz}=1~\mathrm{cycle/s}[/latex]