TABLE OF CONTENTS All the vector operations we have considered thus far are applicable to functions commonly referred to as fields. A field is a function that describes a physical quantity at all points in space. A physical quantity can be either a scalar or a vector; thus, a field can also be a scalar field or a vector field.
A scalar field is specified by a single number at each point. Some well-known examples of scalar fields include temperature and pressure of a gas, the altitude above sea level, and electric potential. For example, in Chapter 3, we will show that the potential distribution within a parallel-plate capacitor (two parallel conducting plates separated by an insulating medium; see Figure 2.17a) is a linear function of the distance between the conducting plates, as illustrated in Figure 2.17b. Thus, the equipotential surfaces are planes parallel to the conductors. By the way, an equipotential surface is a surface on which there is no change in the potential.
A vector field is specified by both a magnitude and a direction at each point in space. The velocity and acceleration of a fluid, the gravitational force, and the electric field within a coaxial cable are some examples of vector fields. We will also show in Chapter 3 that the electric field intensity within a parallel-plate capacitor is constant and is directed from the...
