Electromagnetic waves
At this point in the course we'll move into optics. This might seem like a separate topic from electricity and magnetism, but optics is really a sub-topic of electricity and magnetism. This is because optics deals with the behavior of light, and light is one example of an electromagnetic wave.
Light and other electromagnetic waves
Light is not the only example of an electromagnetic wave. Other electromagnetic waves include the microwaves you use to heat up leftovers for dinner, and the radio waves that are broadcast from radio stations. An electromagnetic wave can be created by accelerating charges; moving charges back and forth will produce oscillating electric and magnetic fields, and these travel at the speed of light. It would really be more accurate to call the speed "the speed of an electromagnetic wave", because light is just one example of an electromagnetic wave. speed of light in vacuum: c = 3.00 x 108 m/s
As we'll go into later in the course when we get to relativity, c is the ultimate speed limit in the universe. Nothing can travel faster than light in a vacuum.
There is a wonderful connection between c, the speed of light in a vacuum, and the constants that appeared in the electricity and magnetism equations, the permittivity of free space and the permeability of free space. James Clerk Maxwell, who showed that all of electricity and magnetism could be boiled down to four basic equations, also worked out that: This clearly shows the link between optics, electricity, and magnetism.
Creating an electromagnetic wave
We've already learned how moving charges (currents) produce magnetic fields. A constant current produces a constant magnetic field, while a changing current produces a changing field. We can go the other way, and use a magnetic field to produce a current, as long as the magnetic field is changing. This is what induced e.m.f is all about. A steadily-changing magnetic field can induce a constant voltage, while an oscillating magnetic field can induce an oscillating voltage.
Focus on these two facts:
1. an oscillating electric field generates an oscillating magnetic field
2. an oscillating magnetic field generates an oscillating electric field
Those two points are key to understanding electromagnetic waves.
An electromagnetic wave (such as a radio wave) propagates outwards from the source (an antenna, perhaps) at the speed of light. What this means in practice is that the source has created oscillating electric and magnetic fields, perpendicular to each other, that travel away from the source. The E and B fields, along with being perpendicular to each other, are perpendicular to the direction the wave travels, meaning that an electromagnetic wave is a transverse wave. The energy of the wave is stored in the electric and magnetic fields.
Properties of electromagnetic waves
Something interesting about light, and electromagnetic waves in general, is that no medium is required for the wave to travel through. Other waves, such as sound waves, can not travel through a vacuum. An electromagnetic wave is perfectly happy to do that.
An electromagnetic wave, although it carries no mass, does carry energy. It also has momentum, and can exert pressure (known as radiation pressure). The reason tails of comets point away from the Sun is the radiation pressure exerted on the tail by the light (and other forms of radiation) from the Sun.
The energy carried by an electromagnetic wave is proportional to the frequency of the wave. The wavelength and frequency of the wave are connected via the speed of light: Electromagnetic waves are split into different categories based on their frequency (or, equivalently, on their wavelength). In other words, we split up the electromagnetic spectrum based on frequency. Visible light, for example, ranges from violet to red. Violet light has a wavelength of 400 nm, and a frequency of 7.5 x 1014 Hz. Red light has a wavelength of 700 nm, and a frequency of 4.3 x 1014 Hz. Any electromagnetic wave with a frequency (or wavelength) between those extremes can be seen by humans.
Visible light makes up a very small part of the full electromagnetic spectrum. Electromagnetic waves that are of higher energy than visible light (higher frequency, shorter wavelength) include ultraviolet light, X-rays, and gamma rays. Lower energy waves (lower frequency, longer wavelength) include infrared light, microwaves, and radio and television waves.
Energy in an electromagnetic wave
The energy in an electromagnetic wave is tied up in the electric and magnetic fields. In general, the energy per unit volume in an electric field is given by: In a magnetic field, the energy per unit volume is: An electromagnetic wave has both electric and magnetic fields, so the total energy density associated with an electromagnetic wave is: It turns out that for an electromagnetic wave, the energy associated with the electric field is equal to the energy associated with the magnetic field, so the energy density can be written in terms of just one or the other: This also implies that in an electromagnetic wave, E = cB.
A more common way to handle the energy is to look at how much energy is carried by the wave from one place to another. A good measure of this is the intensity of the wave, which is the power that passes perpendicularly through an area divided by the area. The intensity, S, and the energy density are related by a factor of c: Generally, it's most useful to use the average power, or average intensity, of the wave. To find the average values, you have to use some average for the electric field E and the magnetic field B. The root mean square averages are used; the relationship between the peak and rms values is: Electromagnetic Spectrum
The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is energy that travels and spreads out as it goes – the visible light that comes from a lamp in your house and the radio waves that come from a radio station are two types of electromagnetic radiation. The other types of EM radiation that make up the electromagnetic spectrum are microwaves, infrared light, ultraviolet light, X-rays and gamma-rays.
You know more about the electromagnetic spectrum than you may think. The image below shows where you might encounter each portion of the EM spectrum in your day-to-day life.

The electromagnetic spectrum from lowest energy/longest wavelength (at the top) to highest energy/shortest wavelength (at the bottom). (Click image for a larger version.)
Radio: Your radio captures radio waves emitted by radio stations, bringing your favorite tunes. Radio waves are also emitted by stars and gases in space.
Microwave: Microwave radiation will cook your popcorn in just a few minutes, but is also used by astronomers to learn about the structure of nearby galaxies.
Infrared: Night vision goggles pick up the infrared light emitted by our skin and objects with heat. In space, infrared light helps us map the dust between stars.
Visible: Our eyes detect visible light. Fireflies, light bulbs, and stars all emit visible light.
Ultraviolet: Ultraviolet radiation is emitted by the Sun and are the reason skin tans and burns. "Hot" objects in space emit UV radiation as well.
X-ray: A dentist uses X-rays to image your teeth, and airport security uses them to see through your bag. Hot gases in the Universe also emit X-rays.
Gamma ray: Doctors use gamma-ray imaging to see inside your body. The biggest gamma-ray generator of all is the Universe.

Is a radio wave the same as a gamma ray?
Are radio waves completely different physical objects than gamma-rays? They are produced in different processes and are detected in different ways, but they are not fundamentally different. Radio waves, gamma-rays, visible light, and all the other parts of the electromagnetic spectrum are electromagnetic radiation.
Electromagnetic radiation can be described in terms of a stream of mass-less particles, called photons, each traveling in a wave-like pattern at the speed of light. Each photon contains a certain amount of energy. The different types of radiation are defined by the the amount of energy found in the photons. Radio waves have photons with low energies, microwave photons have a little more energy than radio waves, infrared photons have still more, then visible, ultraviolet, X-rays, and, the most energetic of all, gamma-rays.
Measuring electromagnetic radiation
Electromagnetic radiation can be expressed in terms of energy, wavelength, or frequency. Frequency is measured in cycles per second, or Hertz. Wavelength is measured in meters. Energy is measured in electron volts. Each of these three quantities for describing EM radiation are related to each other in a precise mathematical way. But why have three ways of describing things, each with a different set of physical units? Comparison of wavelength, frequency and energy for the electromagnetic spectrum. (Click image for a larger version.)
The short answer is that scientists don't like to use numbers any bigger or smaller than they have to. It is much easier to say or write "two kilometers" than "two thousand meters." Generally, scientists use whatever units are easiest for the type of EM radiation they work with.
Astronomers who study radio waves tend to use wavelengths or frequencies. Most of the radio part of the EM spectrum falls in the range from about 1 cm to 1 km, which is 30 gigahertz (GHz) to 100 kilohertz (kHz) in frequencies. The radio is a very broad part of the EM spectrum.
Infrared and optical astronomers generally use wavelength. Infrared astronomers use microns (millionths of a meter) for wavelengths, so their part of the EM spectrum falls in the range of 1 to 100 microns. Optical astronomers use both angstroms (0.00000001 cm, or 10-8 cm) and nanometers (0.0000001, or 10-7, cm). Using nanometers, violet, blue, green, yellow, orange, and red light have wavelengths between 400 and 700 nanometers. (This range is just a tiny part of the entire EM spectrum, so the light our eyes can see is just a little fraction of all the EM radiation around us.
The wavelengths of ultraviolet, X-ray, and gamma-ray regions of the EM spectrum are very small. Instead of using wavelengths, astronomers that study these portions of the EM spectrum usually refer to these photons by their energies, measured in electron volts (eV). Ultraviolet radiation falls in the range from a few electron volts to about 100 eV. X-ray photons have energies in the range 100 eV to 100,000 eV (or 100 keV). Gamma-rays then are all the photons with energies greater than 100 keV
Wavelength (m) Frequency (Hz) Energy (J)
Radio > 1 x 10-1 < 3 x 109 < 2 x 10-24
Microwave 1 x 10-3 - 1 x 10-1 3 x 109 - 3 x 1011 2 x 10-24- 2 x 10-22
Infrared 7 x 10-7 - 1 x 10-3 3 x 1011 - 4 x 1014 2 x 10-22 - 3 x 10-19
Optical 4 x 10-7 - 7 x 10-7 4 x 1014 - 7.5 x 1014 3 x 10-19 - 5 x 10-19
UV 1 x 10-8 - 4 x 10-7 7.5 x 1014 - 3 x 1016 5 x 10-19 - 2 x 10-17
X-ray 1 x 10-11 - 1 x 10-8 3 x 1016 - 3 x 1019 2 x 10-17 - 2 x 10-14
Gamma-ray < 1 x 10-11 > 3 x 1019 > 2 x 10-14
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