# Electromagnetic waves

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 emf 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:
an oscillating electric field generates an oscillating magnetic field
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: