Page 15 - Electromagnetics

Chapter 1

Introductory concepts

1.1 Notation, conventions, and symbology

Any book that covers a broad range of topics will likely harbor some problems with
notation and symbology. This results from having the same symbol used in different areas
to represent different quantities, and also from having too many quantities to represent.
Rather than invent new symbols, we choose to stay close to the standards and warn the
reader about any symbol used to represent more than one distinct quantity.
The basic nature of a physical quantity is indicated by typeface or by the use of a
diacritical mark. Scalars are shown in ordinary typeface: q, , for example. Vectors
¯
are shown in boldface: E, Π. Dyadics are shown in boldface with an overbar: ¯ , A.
Frequency dependent quantities are indicated by a tilde, whereas time dependent quan-
˜
tities are written without additional indication; thus we write E(r,ω) and E(r, t). (Some
quantities, such as impedance, are used in the frequency domain to interrelate Fourier
spectra; although these quantities are frequency dependent they are seldom written in
the time domain, and hence we do not attach tildes to their symbols.) We often combine
diacritical marks:for example, ˜ ¯ denotes a frequency domain dyadic. We distinguish
carefully between phasor and frequency domain quantities. The variable ω is used for
the frequency variable of the Fourier spectrum, while ˇω is used to indicate the constant
frequency of a time harmonic signal. We thus further separate the notion of a phasor
ˇ
field from a frequency domain field by using a check to indicate a phasor field: E(r).
ˇ
˜
However, there is often a simple relationship between the two, such as E = E( ˇω).
We designate the field and source point position vectors by r and r , respectively, and

the corresponding relative displacement or distance vector by R:
R = r − r .

A hat designates a vector as a unit vector (e.g., ˆ x). The sets of coordinate variables in
rectangular, cylindrical, and spherical coordinates are denoted by

(x, y, z), (ρ, φ, z), (r,θ,φ),

respectively. (In the spherical system φ is the azimuthal angle and θ is the polar angle.)
We freely use the “del” operator notation ∇ for gradient, curl, divergence, Laplacian,
and so on.
The SI (MKS) system of units is employed throughout the book.

© 2001 by CRC Press LLC