# 1.2 Dimensions, Units, and Notation

The International System of Units, abbreviated SI after its French name Système Internationale, is the standard system used in today’s scientific literature for expressing the units of physical quantities. Length is a dimension and meter is the unit by which it is expressed relative to a reference standard. The SI system is based on the units for the seven fundamental dimensions listed in Table 1-1. The units for all other dimensions are regarded as secondary because they are based on, and can be expressed in terms of, the seven fundamental units. Appendix A contains a list of quantities used in this book, together with their symbols and units.

# Table 1-1 Fundamental SI units.

Table 1 1 Full Alternative Text

For quantities ranging in value between 10−18 and 10 18, a set of prefixes arranged in steps of 10 3 are commonly used to denote multiples and submultiples of units. These prefixes, all of which were derived from Greek, Latin, Spanish, and Danish terms, are listed in Table 1-2. A length of 5×10−9 m, for example, may be written as 5 nm.

# Table 1-2 Multiple and submultiple prefixes.

Table 1 2 Full Alternative Text

In EM, we work with scalar and vector quantities. In this book we use a medium-weight italic font for symbols denoting scalar quantities, such as R for resistance, and a boldface roman font for symbols denoting vectors, such as E for the electric field vector. A vector consists of a magnitude (scalar) and a direction, with the direction usually denoted by a unit vector. For example,

E=x^E,(1.1)

where E is the magnitude of E and x^ is its direction. A symbol denoting a unit vector is printed in boldface with a circumflex (^) above it.

Throughout this book, we make extensive use of phasor representation in solving problems involving electromagnetic quantities that vary sinusoidally in time. Letters denoting phasor quantities are printed with a tilde (∼) over the letter. Thus, E˜ is the phasor electric field vector corresponding to the instantaneous electric field vector E(t). This notation is discussed in more detail in Section 1-7.