It had been known since the early 19th century, from experiments with interference and diffraction, that light is a wave, but no one understood what was “waving.” Faraday speculated that light was somehow connected to electricity and magnetism, but Maxwell was the first to understand not only that light is an electromagnetic wave but also that electromagnetic waves can exist at any frequency, not just the frequencies of visible light.

In the previous section, we used Maxwell’s equations to discover that:

1. Maxwell’s equations predict the existence of sinusoidal electromagnetic waves that travel through empty space independent of any charges or currents.

2. The waves are transverse waves, with $\vec{E}$ and $\vec{B}$ perpendicular to the direction of propagation $\vec{v}{}_{\text{em}}$.

3. $\vec{E}$ and $\vec{B}$ are perpendicular to each other in a manner such that $\vec{E}\times \vec{B}$ is in the direction of $\vec{v}{}_{\text{em}}$.

4. All electromagnetic waves, regardless of frequency or wavelength, travel in vacuum at speed $v_{\text{em}}=1/\sqrt{{ϵ}_0{\mu }_0}=c$, the speed of light.

5. The field strengths are related by $E=cB$ at every point on the wave.

FIGURE 31.23 illustrates many of these characteristics of electromagnetic waves. It’s a useful picture, and one that you’ll see in any textbook, but a picture that can be very misleading if you don’t think about it carefully. First and foremost, $\vec{E}$ and $\vec{B}$ are not spatial vectors. That is, they don’t stretch spatially in the y- or z-direction for a certain distance. Instead, these vectors are showing the field strengths and directions along a single line, the x-axis. An $\vec{E}$ vector pointing in the y-direction is saying, “At this point on the x-axis, where the tail is, this is the direction and strength of the electric field.” Nothing is “reaching” to a point in space above the x-axis.

FIGURE 31.23 A sinusoidal electromagnetic wave.

Second, we’re assuming this is a plane wave, which, you’ll recall, is a wave for which the fields are the same everywhere in any plane perpendicular to $\vec{v}{}_{\text{em}}$. Figure 31.23 shows the fields only along one line. But whatever the fields are doing at a point on the x-axis, they are doing the same thing everywhere in the yz-plane that slices the x-axis at that point. With this in mind, let’s explore some other properties of electromagnetic waves.