# PHYS 2212 Module 12

12: Electromagnetic Waves

The pressure from sunlight predicted by Maxwell’s equations helped produce the tail of Comet McNaught. (credit: modification of work by Sebastian Deiries—ESO)

Our view of objects in the sky at night, the warm radiance of sunshine, the sting of sunburn, our cell phone conversations, and the X-rays revealing a broken bone—all are brought to us by electromagnetic waves. It would be hard to overstate the practical importance of electromagnetic waves, through their role in vision, through countless technological applications, and through their ability to transport the energy from the Sun through space to sustain life and almost all of its activities on Earth.

Theory predicted the general phenomenon of electromagnetic waves before anyone realized that light is a form of an electromagnetic wave. In the mid-nineteenth century, James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects known at that time. Maxwell’s equations, summarizing this theory, predicted the existence of electromagnetic waves that travel at the speed of light. His theory also predicted how these waves behave, and how they carry both energy and momentum. The tails of comets, such as Comet McNaught in Figure 16.1, provide a spectacular example. Energy carried by light from the Sun warms the comet to release dust and gas. The momentum carried by the light exerts a weak force that shapes the dust into a tail of the kind seen here. The flux of particles emitted by the Sun, called the solar wind, typically produces an additional, second tail, as described in detail in this chapter.

In this module, we explain Maxwell’s theory and show how it leads to his prediction of electromagnetic waves. We use his theory to examine what electromagnetic waves are, how they are produced, and how they transport energy and momentum. We conclude by summarizing some of the many practical applications of electromagnetic waves.

During this course, you have learned a whole lot about electric fields and magnetic fields. And up until now, we’ve kept these concepts mostly separate from each other. But now we get to bring them together in our discussion of electromagnetic waves.

We defined an electric force and a magnetic force, but in actuality they are one in the same — it’s an electromagnetic interaction. It was easier to learn these concepts separately but you can’t have one without the other.

What we will do in this module is describe how electric fields and magnetic fields combine to form an electromagnetic wave. What’s really neat about this is electromagnetic (or EM, for short) waves create EM radiation like x-rays, gamma rays, infrared, and radio waves. But visible light is also electromagnetic radiation. This is one of the coolest things about this course in physics: light is made from electric fields and magnetic fields that propagate through space.

In this short video, Professor Dave explains EM waves:

We’ve seen some of the ideas/discoveries of Ampere, Faraday, and others. So far, we’ve treated E and B as distinct (if related). But, in what is perhaps one of a small handful of truly triumphant intellectual breakthroughs in the history of physics, James Clerk Maxwell (a Scot, in the mid 1800’s) put it all together and came up with the four equations which described all electromagnetic phenomena! We’ve seen most of them already:

Gauss’s Law, charges create E-fields, in specific “patterns.” E-fields superpose.

Gauss’s Law for magnetism, there are no magnetic monopoles and B-fields are always closed loops.

Faraday’s Law of induction, a changing B-field induces an E-field.

Ampere-Maxwell law, we’ve seen the first part of this (Ampere’s law) but now we will talk about the other part that Maxwell added. But what this equation says is a current can induce a B-field AND a changing E-field can also induce a B-field.

This last piece was Maxwell’s insight. It was not based on experiments (like all the rest). Maxwell argued as a “theorist”, arguing from mathematical symmetry. (It was only later demonstrated in the lab.) We’ll discuss it soon.

#### 12.1 Maxwell’s Equations and Electromagnetic Waves

• Explain Maxwell’s correction of Ampère’s law by including the displacement current
• State and apply Maxwell’s equations in integral form
• Describe how the symmetry between changing electric and changing magnetic fields explains Maxwell’s prediction of electromagnetic waves
• Describe how Hertz confirmed Maxwell’s prediction of electromagnetic waves

#### 12.2 Plane Electromagnetic Waves

• Describe how Maxwell’s equations predict the relative directions of the electric fields and magnetic fields, and the direction of propagation of plane electromagnetic waves
• Explain how Maxwell’s equations predict that the speed of propagation of electromagnetic waves in free space is exactly the speed of light
• Calculate the relative magnitude of the electric and magnetic fields in an electromagnetic plane wave
• Describe how electromagnetic waves are produced and detected

#### 12.3 Energy Carried by Electromagnetic Waves

• Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes
• Calculate the Poynting vector and the energy intensity of electromagnetic waves
• Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequency

#### 12.4 Momentum and Radiation Pressure

• Describe the relationship of the radiation pressure and the energy density of an electromagnetic wave
• Explain how the radiation pressure of light, while small, can produce observable astronomical effects

#### 12.5 The Electromagnetic Spectrum

• Explain how electromagnetic waves are divided into different ranges, depending on wavelength and corresponding frequency
• Describe how electromagnetic waves in different categories are produced
• Describe some of the many practical everyday applications of electromagnetic waves