14.7. A Modern Summary of Maxwell’s Results

Maxwell not only unified three different fields into a single theory, but his prediction was that there were entirely new electromagnetic wave phenomena beyond just what we can visibly see with our eyes. In fact, “light” is only a tiny portion of what’s called the Electromagnetic Spectrum. Here it is in all of its glory:

An electromagnetic wave (E&M wave) is a transverse wave with two coupled amplitudes of an electric and magnetic field vector traveling at a single speed, that of light: \(c=3 \times 10^8\)m/s. Your cell phone signal? E&M waves. The light through your window? E&M waves. The warmth you feel on (and radiate from) your skin. Yup, E&M waves. Back and forth. We’ll see that even the teenage Einstein found a contradiction here that in part stimulated his venture into Special Relativity.

You shield yourself from the sun’s rays because not only does the sun shine visibly, but it emits short-wavelength electromagnetic waves which we call “ultraviolet.” Something is hot–and you’re warm–because any object and you emit infrared radiation which we perceive of as heat. In fact everything in your life emits radiation of all different sorts and all of them are identical in one important way:

Note

All electromagnetic waves travel at the speed of light.

Because any wave’s speed, frequency, and wavelength are all related by one simple relation:

\[ c=f\lambda \]

the only thing that distinguishes the color blue from infrared waves or radio waves or microwaves are their wavelengths, or equivalently, their frequencies–again, because they all move at the same speed.

Now that’s we’re friendly with Electromagnetism, we can call it by its nickname: EM.