Electromagnetic Waves

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Abstract

The waves we've dealt with so far in this book have been fairly easy to visualize. Waves involving springs/masses, strings, and air molecules are things we can apply our intuition to. But we'll now switch gears and talk about electromagnetic waves. These are harder to get a handle on, for a number of reasons. First, the things that are oscillating are electric and magnetic fields, which are much harder to see (which is an ironic statement, considering that we see with light, which is an electromagnetic wave). Second, the fields can have components in various directions, and there can be relative phases between these components (this will be important when we discuss polarization). And third, unlike all the other waves we've dealt with, electromagnetic waves don't need a medium to propagate in. They work just fine in vacuum. In the late 1800's, it was generally assumed that electromagnetic waves required a medium, and this hypothesized medium was called the " ether. " However, no one was ever able to observe the ether. And for good reason, because it doesn't exist. This chapter is a bit long. The outline is as follows. In Section 8.1 we talk about waves in an extended LC circuit, which is basically what a coaxial cable is. We find that the system supports waves, and that these waves travel at the speed of light. This section serves as motivation for the fact that light is an electromagnetic wave. In Section 8.2 we show how the wave equation for electromagnetic waves follows from Maxwell's equations. Maxwell's equations govern all of electricity and magnetism, so it is no surprise that they yield the wave equation. In Section 8.3 we see how Maxwell's equations constrain the form of the waves. There is more information contained in Maxwell's equations than there is in the wave equation. In Section 8.4 we talk about the energy contained in an electromagnetic wave, and in particular the energy flow which is described by the Poynting vetor. In Section 8.5 we talk about the momentum of an electromagnetic wave. We saw in Section 4.4 that the waves we've discussed so far carry energy but not momentum. Electromagnetic waves carry both. 1 In Section 8.6 we discuss polarization, which deals with the relative phases of the different components of the electric (and magnetic) field. In Section 8.7 we show how an electromagnetic wave can be produced by an oscillating (and hence accelerating) charge. Finally, in Section 8.8 we discuss the reflection and transmission that occurs when an electromagnetic wave encounters the boundary between two different regions, such as air 1 Technically, all waves carry momentum, but this momentum is suppressed by a factor of v/c, where v is the speed of the wave and c is the speed of light. This follows from the relativity fact that energy is equivalent to mass. So a flow of energy implies a flow of mass, which in turn implies nonzero momentum. However, the factor of v/c causes the momentum to be negligible unless we're dealing with relativistic speeds.

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APA

Sangster, A. J. (2014). Electromagnetic Waves. Green Energy and Technology, 194, 27–50. https://doi.org/10.1007/978-3-319-08512-8_2

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