Engineering and Applied Sciences Applied Physics 216 Lecture 21: Lecture 21
21 Feb 2017
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Document Summary
There are a few ways to introduce the idea of an harmonic electromagnetic plane wave to you. The standard way is to tell you that they are solutions to maxwell"s homogeneous equations. These are the maxwell equations in some region of space where there is no charge or current density. I then tell you lets see if we can find wave solutions of the form. 0 r i k t (2) (3) ane waves . k is called the (wave vector) and are called the complex amplitudes. and. I remind you that the complex quantity i k r t k r t k r. )t (4) i e c (os in s. A simple proof follows by making representing both sides by power series expansions and equating the real and imaginary parts. The complex exponential also satisfies the same linear ordinary differential equation with respect to time as does its related sine and cosine function.
