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13.3Electromagnetic waves

Each and every one of us is irradiated by electromagnetic (EM) waves a transverse wave moving at the speed of light in vacuum and consisting of oscillations of an electric and a magnetic field at right angles to each other from a lots of different sources: radio and television stations, mobile phones and base station antennas, from doctors’ and dentists’ X-ray machines, the sun, computer screens, light bulbs and so on. Unlike mechanical waves that require a medium, EM waves can travel in vacuum.

It was the towering achievement of J.C. Maxwell in the mid-1800s to predict the existence of a new, special kind of wave—electromagnetic waves—of which visible light is a very small but important part. What Maxwell showed is that an oscillating electric field produces an oscillating magnetic field (see Chapters 18–20) such that the two are at right angles to each other and both propagate in space at the speed of light (Figure 13.26).

Figure 13.26: An EM wave propagating along the direction of the x-axis. The electric and magnetic fields are in phase, i.e. they have matching crests, troughs and zeroes. The two fields are at right angles to each other at all times.

The huge family of EM waves consists of many waves of different wavelength (and hence also frequency), as shown in Figure 13.27.

Figure 13.27: The electromagnetic spectrum.

What all EM waves have in common is that they move at the speed of light in a vacuum. That speed is (exactly) c = 299 792 458 m s−1 or approximately 3.00 × 108 m s−1. According to Einstein’s relativity theory this is the limiting speed for anything moving through space. Maxwell’s theory predicts that the speed of light is not affected by the speed of its source—a very curious fact. Einstein used this fact as one of the building blocks of his theory of relativity.

Since both the electric and the magnetic field making up the EM wave are at right angles to the direction of energy transfer of the wave, EM waves are transverse.

Electromagnetic waves are produced when electric charges accelerate or during transitions in molecular, atomic or nuclear energy levels (see Chapters 21–25).

CHECK YOURSELF 4

State two differences between an electromagnetic wave and a sound wave.

Worked Example 13.6

A radio station emits at a frequency of 90.8 MHz. What is the wavelength of the waves emitted?

Answer

The waves emitted are electromagnetic waves and move at the speed of light (3 × 108 m s−1). Therefore, from c = f λ we find λ = 3.3 m.

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In mechanical waves a medium is always required for the wave to propagate through. In that case the displacement of the wave is the actual displacement of the particles of the medium which perform simple harmonic oscillations about their equilibrium positions. By definition, then, a mechanical wave cannot travel in vacuum. An electromagnetic wave can because the displacement in this case is not that of a material object but rather the oscillation of something much more abstract: a field. Specifically, electric and magnetic fields. We will discuss fields in detail in Unit D.

TEST YOUR UNDERSTANDING

17Give one example that shows that EM waves carry energy.

18Explain why we call EM waves transverse.

19Recall Wien’s law from Chapter 7.3. The universe is filled with EM waves at a temperature of 2.7 K. What part of the EM spectrum do these waves belong to?

20The distance between the earth and the sun is 1.5 × 1011 m. How long does light take to travel to earth from the sun?