Page 127 - Engineering Electromagnetics, 8th Edition

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CHAPTER

Conductors and

Dielectrics

n this chapter, we apply the methods we have learned to some of the materials
with which an engineer must work. In the first part of the chapter, we consider
I conducting materials by describing the parameters that relate current to an applied
electric field. This leads to a general definition of Ohm’s law. We then develop methods
of evaluating resistances of conductors in a few simple geometric forms. Conditions
that must be met at a conducting boundary are obtained next, and this knowledge
leads to a discussion of the method of images. The properties of semiconductors are
described to conclude the discussion of conducting media.
In the second part of the chapter, we consider insulating materials, or dielectrics.
Such materials differ from conductors in that ideally, there is no free charge that can be
transported within them to produce conduction current. Instead, all charge is confined
to molecular or lattice sites by coulomb forces. An applied electric field has the effect
of displacing the charges slightly, leading to the formation of ensembles of electric
dipoles. The extent to which this occurs is measured by the relative permittivity, or
dielectric constant. Polarization of the medium may modify the electric field, whose
magnitude and direction may differ from the values it would have in a different
medium or in free space. Boundary conditions for the fields at interfaces between
dielectrics are developed to evaluate these differences.
It should be noted that most materials will possess both dielectric and conductive
properties; that is, a material considered a dielectric may be slightly conductive, and
a material that is mostly conductive may be slightly polarizable. These departures
from the ideal cases lead to some interesting behavior, particularly as to the effects
on electromagnetic wave propagation, as we will see later. ■

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