RF/Microwave Engineering and Applications in Energy Systems. Abdullah Eroglu

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1 Fundamentals of Electromagnetics

      1.1 Introduction

      The fundamentals of electromagnetics constitute steps toward the advancement of technology in communication, radar, and energy and power applications. In this chapter, some important theorems and mathematical concepts are discussed with examples.

1.2 Line, Surface, and Volume Integrals

      1.2.1 Vector Analysis

A scalar quantity gives us a single value of some variable for every point in space such as voltage, current, energy, and temperature. A vector is a quantity which has both a magnitude and a direction in space. Velocity, momentum, acceleration, and force are examples of vector quantities. A mathematical representation of a vector is given in (1.1).

(1.1)

A vector can be represented as a directed line segment, as shown in Figure 1.1.

      In Figure 1.1, the magnitude of the vector is given by |A|. The unit vector which defines the direction of the vector is given by

      (1.2)

      You may consider falling snowflakes as an example for a vector which has direction and magnitude.

      1.2.1.1 Unit Vector Relationship

It is frequently useful to resolve vectors into components along the axial direction using general unit vectors, as given by (1.3)

(1.3)

Then

      (1.4a)

      (1.4b)

      (1.4c)

Figure 1.1 Vector representation.

      In Cartesian coordinate system, unit vectors are defined as

      (1.5)

      So

      (1.6a)

      (1.6b)

      (1.6c)

      In a cylindrical coordinate system, unit vectors are defined as

      (1.7)

      Hence

      (1.8a)

      (1.8b)

      (1.8c)СКАЧАТЬ