In 1855, less than two years after receiving his undergraduate degree, the Scottish physicist James Clerk Maxwell presented a paper titled “On Faraday’s Lines of Force.” In this paper, he began to sketch out how Faraday’s pictorial ideas about fields could be given a rigorous mathematical basis. Maxwell was troubled by a certain lack of symmetry. Faraday had found that a changing magnetic field creates an induced electric field, a non-Coulomb electric field not tied to charges. But what, Maxwell began to wonder, about a changing electric field?

To complete the symmetry, Maxwell proposed that a changing electric field creates an induced magnetic field, a new kind of magnetic field not tied to the existence of currents. FIGURE 30.33 shows a region of space where the electric field is increasing. This region of space, according to Maxwell, is filled with a pinwheel pattern of induced magnetic fields. The induced magnetic field looks like the induced electric field, with $\vec{E}$ and $\vec{B}$ interchanged, except that—for technical reasons explored in the next chapter—the induced $\vec{B}$ points the opposite way from the induced $\vec{E}$. Although there was no experimental evidence that induced magnetic fields existed, Maxwell went ahead and included them in his electromagnetic field theory. This was an inspired hunch, soon to be vindicated.

FIGURE 30.33 Maxwell hypothesized the existence of induced magnetic fields.

Full Alternative Text

Maxwell soon realized that it might be possible to establish self-sustaining electric and magnetic fields that would be entirely independent of any charges or currents. That is, a changing electric field $\vec{E}$ creates a magnetic field $\overrightarrow{B}$, which then changes in just the right way to recreate the electric field, which then changes in just the right way to again recreate the magnetic field, and so on. The fields are continually recreated through electromagnetic induction without any reliance on charges or currents.

Maxwell was able to predict that electric and magnetic fields would be able to sustain themselves, free from charges and currents, if they took the form of an electromagnetic wave. The wave would have to have a very specific geometry, shown in FIGURE 30.34, in which $\vec{E}$ and $\vec{B}$ are perpendicular to each other as well as perpendicular to the direction of travel. That is, an electromagnetic wave would be a transverse wave.

FIGURE 30.34 A self-sustaining electromagnetic wave.

Furthermore, Maxwell’s theory predicted that the wave would travel with speed

where ${\epsilon }_0$ is the permittivity constant from Coulomb’s law and ${\mu }_0$ is the permeability constant from the law of Biot and Savart. Maxwell computed that an electromagnetic wave, if it existed, would travel with speed $v_{\text{em }\text{wave}}=3.00\times {10}^8\text{m}\text{/}\text{s}$.

We don’t know Maxwell’s immediate reaction, but it must have been both shock and excitement. His predicted speed for electromagnetic waves, a prediction that came directly from his theory, was none other than the speed of light! This agreement could be just a coincidence, but Maxwell didn’t think so. Making a bold leap of imagination, Maxwell concluded that light is an electromagnetic wave.

It took 25 more years for Maxwell’s predictions to be tested. In 1886, the German physicist Heinrich Hertz discovered how to generate and transmit radio waves. Two years later, in 1888, he was able to show that radio waves travel at the speed of light. Maxwell, unfortunately, did not live to see his triumph. He had died in 1879, at the age of 48.