Page 20 - Electromagnetics Handbook

other, and so first described the principle of charge conservation. Twentieth century
physics has added dramatically to the understanding of charge:

1. Electric charge is a fundamental property of matter, as is mass or dimension.
2. Charge is quantized:there exists a smallest quantity (quantum) of charge that
can be associated with matter. No smaller amount has been observed, and larger
amounts always occur in integral multiples of this quantity.
3. The charge quantum is associated with the smallest subatomic particles, and these
particles interact through electrical forces. In fact, matter is organized and arranged
through electrical interactions; for example, our perception of physical contact is
merely the macroscopic manifestation of countless charges in our fingertips pushing
against charges in the things we touch.
4. Electric charge is an invariant:the value of charge on a particle does not depend on
the speed of the particle. In contrast, the mass of a particle increases with speed.
5. Charge acts as the source of an electromagnetic field; the field is an entity that can
carry energy and momentum away from the charge via propagating waves.

We begin our investigation of the properties of the electromagnetic field with a detailed
examination of its source.

1.3.1 Macroscopic electromagnetics
We are interested primarily in those electromagnetic effects that can be predicted by
classical techniques using continuous sources (charge and current densities). Although
macroscopic electromagnetics is limited in scope, it is useful in many situations en-
countered by engineers. These include, for example, the determination of currents and
voltages in lumped circuits, torques exerted by electrical machines, and fields radiated by
antennas. Macroscopic predictions can fall short in cases where quantum effects are im-
portant:e.g., with devices such as tunnel diodes. Even so, quantum mechanics can often
be coupled with classical electromagnetics to determine the macroscopic electromagnetic
properties of important materials.
Electric charge is not of a continuous nature. The quantization of atomic charge —
±e for electrons and protons, ±e/3 and ±2e/3 for quarks — is one of the most precisely
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established principles in physics (verified to 1 part in 10 ). The value of e itself is known
to great accuracy:

e = 1.60217733 × 10 −19 Coulombs (C).
However, the discrete nature of charge is not easily incorporated into everyday engineer-
ing concerns. The strange world of the individual charge — characterized by particle
spin, molecular moments, and thermal vibrations — is well described only by quantum
theory. There is little hope that we can learn to describe electrical machines using such
concepts. Must we therefore retreat to the macroscopic idea and ignore the discretization
of charge completely? A viable alternative is to use atomic theories of matter to estimate
the useful scope of macroscopic electromagnetics.
Remember, we are completely free to postulate a theory of nature whose scope may
be limited. Like continuum mechanics, which treats distributions of matter as if they
were continuous, macroscopic electromagnetics is regarded as valid because it is verified
by experiment over a certain range of conditions. This applicability range generally
corresponds to dimensions on a laboratory scale, implying a very wide range of validity
for engineers.

© 2001 by CRC Press LLC