Page 103 - Electromagnetics

The dynamic coupling between the various field vectors in Maxwell’s equations provides
a means of characterizing the field. Static fields are characterized by decoupling of the
electric and magnetic fields. Quasistatic fields exhibit some coupling, but the wave
characteristic of the field is ignored. Tightly coupled fields are dominated by the wave
effect, but may still show a static-like spatial distribution near the source. Any such
“near-zone” effects are generally ignored for fields at light-wave frequencies, and the
particle nature of light must often be considered.

2.10.1 Electromagnetic waves
An early result of Maxwell’s theory was the prediction and later verification by Heinrich
Hertz of the existence of electromagnetic waves. We now know that nearly any time-
varying source produces waves, and that these waves have certain important properties.
An electromagnetic wave is a propagating electromagnetic field that travels with finite
velocity as a disturbance through a medium. The field itself is the disturbance, rather
than merely representing a physical displacement or other effect on the medium. This fact
is fundamental for understanding how electromagnetic waves can travel through a true
vacuum. Many specific characteristics of the wave, such as velocity and polarization,
depend on the properties of the medium through which it propagates. The evolution
of the disturbance also depends on these properties: we say that a material exhibits
“dispersion” if the disturbance undergoes a change in its temporal behavior as the wave
progresses. As waves travel they carry energy and momentum away from their source.
This energy may be later returned to the source or delivered to some distant location.
Waves are also capable of transferring energy to, or withdrawing energy from, the medium
through which they propagate. When energy is carried outward from the source never
to return, we refer to the process as “electromagnetic radiation.” The effects of radiated
fields can be far-reaching; indeed, radio astronomers observe waves that originated at the
very edges of the universe.
Light is an electromagnetic phenomenon, and many of the familiar characteristics of
light that we recognize from our everyday experience may be applied to all electromag-
netic waves. For instance, radio waves bend (or “refract”) in the ionosphere much as
light waves bend while passing through a prism. Microwaves reflect from conducting sur-
faces in the same way that light waves reflect from a mirror; detecting these reflections
forms the basis of radar. Electromagnetic waves may also be “confined” by reflecting
boundaries to form waves standing in one or more directions. With this concept we can
use waveguides or transmission lines to guide electromagnetic energy from spot to spot,
or to concentrate it in the cavity of a microwave oven.
The manifestations of electromagnetic waves are so diverse that no one book can
possibly describe the entire range of phenomena or application. In this section we shall
merely introduce the reader to some of the most fundamental concepts of electromagnetic
wave behavior. In the process we shall also introduce the three most often studied types
of traveling electromagnetic waves: plane waves, spherical waves, and cylindrical waves.
In later sections we shall study some of the complicated interactions of these waves with
objects and boundaries, in the form of guided waves and scattering problems.
Mathematically, electromagnetic waves arise as a subset of solutions to Maxwell’s equa-
tions. These solutions obey the electromagnetic “wave equation,” which may be derived
from Maxwell’s equations under certain circumstances. Not all electromagnetic fields
satisfy the wave equation. Obviously, time-invariant fields cannot represent evolving
wave disturbances, and must obey the static field equations. Time-varying fields in cer-

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