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Über dieses Buch

This text provides students with the missing link that can help them master the basic principles of electromagnetics. The concept of vector fields is introduced by starting with clear definitions of position, distance, and base vectors. The symmetries of typical configurations are discussed in detail, including cylindrical, spherical, translational, and two-fold rotational symmetries. To avoid serious confusion between symbols with two indices, the text adopts a new notation: a letter with subscript 1-2 for the work done in moving a unit charge from point 2 to point 1, in which the subscript 1-2 mimics the difference in potentials, while the hyphen implies a sense of backward direction, from 2 to 1. This text includes 300 figures in which real data are drawn to scale. Many figures provide a three-dimensional view. Each subsection includes a number of examples that are solved by examining rigorous approaches in steps. Each subsection ends with straightforward exercises and answers through which students can check if they correctly understood the concepts. A total 350 of examples and exercises are provided. At the end of each section, review questions are inserted to point out key concepts and relations discussed in the section. They are given with hints referring to the related equations and figures. The book contains a total of 280 end-of-chapter problems.

Inhaltsverzeichnis

Frontmatter

Vector Algebra and Coordinate Systems

Abstract
Electromagnetics entails the study of electric and magnetic phenomena in free space and material media. Electromagnetics comprises three branches: electrostatics concerning static electric fields, magnetostatics concerning static magnetic fields, and electrodynamics concerning time-varying electric and magnetic fields. Electromagnetic theories are based on electromagnetic models that consist of sources such as electric charges and currents, basic quantities such as electric and magnetic field intensities, rules of operations such as vector algebra and coordinate systems, and fundamental laws such as Coulomb’s law and Maxwell’s equations. The first two chapters of the text discuss the rules of operation, including vector algebra, coordinates systems, and vector calculus.
Yeon Ho Lee

Vector Calculus

Abstract
In Chapter 1, we discussed the basic concepts of vector algebra developed in the three common coordinate systems. Through the use of the position and base vectors, we could specify points and vectors in three-dimensional space. We reviewed typical symmetries of vector fields that easily reveal themselves in the cylindrical and spherical coordinate systems. We defined differential quantities such as differential length vectors, differential area vectors, and differential volumes in different coordinate systems. We also learned how to transform the coordinates of a point or the components of a vector from one coordinate system to another.
Yeon Ho Lee

Electrostatics

Abstract
In the first two chapters, we discussed in detail mathematical topics, such as vector algebra, coordinate systems, and vector calculus, which provide essential tools for the study of electromagnetics. We are now ready to study the basic concepts of electromagnetics and learn about their applications. This chapter focuses on electrostatics, which deals with static electric fields induced by static electric charges. The static electric fields and charges are constant in time, although they may vary in space. In the present chapter, we will see that all discussions of static electric fields can be boiled down to the divergence and the curl of the electric field. They are two fundamental relations in the sense that they allow us to uniquely determine a static electric field in a given region of space according to Helmholtz’s theorem.
Yeon Ho Lee

Steady Electric Current

Abstract
In the previous chapter, we focused our attention on static electric charges that are fixed in space and constant in time. Otherwise, we assumed that the charges relax to a steady distribution in an instant. Electric charges, however, can move under the influence of an electric field. The charges moving in a conductor constitute a conduction current, while those moving in a vacuum constitute a convection current. From basic circuit theory, the readers should be familiar with the conduction current flowing in a simple electric circuit, which is governed by Ohm’s law, stating that the voltage across a resistor is equal to the product of the resistance and the current passing through it. According to the principle of conservation of charge, electric charges cannot be created or destroyed.
Yeon Ho Lee

Magnetostatics

Abstract
In Chapter 3, we focused our discussions on electrostatics, which is primarily concerned with the electric field E and electric flux density D. Initially, we introduced the electric field to describe the interaction between static electric charges separated by free space. We defined the electric flux density to account for the interaction between an external electric field and a material medium.
Yeon Ho Lee

Time-Varying Fields and Maxwell’s Equations

Abstract
Until now, we have devoted ourselves to static electric and static magnetic fields that are constant in time. To summarize the discussions up to this point, the electric field and electric flux density due to a distribution of static electric charges are related by the constitutive relation D = ε E , from which we define the permittivity of the material.
Yeon Ho Lee

Wave Motion

Abstract
A wave is the disturbance of a medium that travels through space with no change in its shape. A mechanical wave in a stretched spring, a water wave on the surface of a lake, and a sound wave in the air are good examples of traveling waves. There are two types of traveling waves. For instance, the wave in a spring as shown in Fig. 7.1(a) is a longitudinal wave for which the medium is displaced in the same direction as the direction of propagation of the wave. The other wave as shown in Fig. 7.1(b) is a transverse wave for which the medium is displaced in the direction perpendicular to the direction of propagation of the wave.
Yeon Ho Lee

Time-Harmonic Electromagnetic Waves

Abstract
We saw in Chapter 7 that Maxwell’s equations can be combined into the differential wave equations for the electric field \(\mathcal{E}\) and the magnetic field \(\mathcal{H}\). Since \(\mathcal{E}\) and \(\mathcal{H}\) are interrelated under time-varying conditions, the differential wave equation for \(\mathcal{E}\) alone is enough to describe the general behavior of an electromagnetic wave propagating in a region of space.
Yeon Ho Lee

Transmission Lines

Abstract
So far most discussion of electromagnetic waves was in a medium of infinite extent, or two semi-infinite media adjoined to each other. By solving the differential wave equation we saw that the electromagnetic waves take the form of a uniform plane wave in such media. The uniform plane wave is an unbounded and unguided wave in the sense that the electric field exists in all space and the electromagnetic energy spreads over the whole space. While an unbounded and unguided wave may be useful for broadcasting radio and TV signals, it is inefficient when used for point-to-point transmission of electromagnetic power or information.
Yeon Ho Lee

Waveguides

Abstract
In Chapter 9, we saw that a transmission line is used in transmitting electromagnetic signals from a point to anther by means of a transverse electromagnetic (TEM) wave. At an operating frequency in the SHF (3-30[GHz]) or EHF (30- 300[GHz]) bands, the two-conductor transmission line becomes highly lossy owing to the skin effect in the conductors with a finite conductivity. Alternatively, waveguides can provide a much more efficient way of transmitting electromagnetic signals with the frequency in those bands.
Yeon Ho Lee

Backmatter

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