Page 385 - Engineering Electromagnetics, 8th Edition

11

CHAPTER

The Uniform

Plane Wave

his chapter is concerned with the application of Maxwell’s equations to the
problem of electromagnetic wave propagation. The uniform plane wave rep-
T resents the simplest case, and while it is appropriate for an introduction, it is
of great practical importance. Waves encountered in practice can often be assumed
to be of this form. In this study, we will explore the basic principles of electromag-
netic wave propagation, and we will come to understand the physical processes that
determine the speed of propagation and the extent to which attenuation may occur.
We will derive and use the Poynting theorem to find the power carried by a wave.
Finally, we will learn how to describe wave polarization. ■

11.1 WAVE PROPAGATION IN FREE SPACE
We begin with a quick study of Maxwell’s equations, in which we look for clues
of wave phenomena. In Chapter 10, we saw how voltages and currents propagate as
wavesin transmission lines, and we know that the existence of voltages and currents
implies the existence of electric and magnetic fields. So we can identify a transmission
line as a structure that confines the fields while enabling them to travel along its length
as waves. It can be argued that it is the fields that generate the voltage and current
in a transmission line wave, and—if there is no structure on which the voltage and
current can exist—the fields will exist nevertheless, and will propagate. In free space,
the fields are not bounded by any confining structure, and so they may assume any
magnitude and direction, as initially determined by the device (such as an antenna)
that generates them.
When considering electromagnetic waves in free space, we note that the medium
is sourceless (ρ ν = J = 0). Under these conditions, Maxwell’s equations may be

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