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chapter 09

# chapter 09 - PART 4 WAVES A N D APPLICATIONS Chapter y...

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PART 4 WAVES AND APPLICATIONS

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Chapter y MAXWELL'S EQUATIONS Do you want to be a hero? Don't be the kind of person who watches others do great things or doesn't know what's happening. Go out and make things happen. The people who get things done have a burning desire to make things happen, get ahead, serve more people, become the best they can possibly be, and help improve the world around them. —GLENN VAN EKEREN 9.1 INTRODUCTION In Part II (Chapters 4 to 6) of this text, we mainly concentrated our efforts on electrostatic fields denoted by E(x, y, z); Part III (Chapters 7 and 8) was devoted to magnetostatic fields represented by H(JC, y, z). We have therefore restricted our discussions to static, or time- invariant, EM fields. Henceforth, we shall examine situations where electric and magnetic fields are dynamic, or time varying. It should be mentioned first that in static EM fields, electric and magnetic fields are independent of each other whereas in dynamic EM fields, the two fields are interdependent. In other words, a time-varying electric field necessarily involves a corresponding time-varying magnetic field. Second, time-varying EM fields, represented by E(x, y, z, t) and H(x, y, z, t), are of more practical value than static EM fields. However, familiarity with static fields provides a good background for understand- ing dynamic fields. Third, recall that electrostatic fields are usually produced by static elec- tric charges whereas magnetostatic fields are due to motion of electric charges with uniform velocity (direct current) or static magnetic charges (magnetic poles); time-varying fields or waves are usually due to accelerated charges or time-varying currents such as shown in Figure 9.1. Any pulsating current will produce radiation (time-varying fields). It is worth noting that pulsating current of the type shown in Figure 9.1(b) is the cause of ra- diated emission in digital logic boards. In summary: charges —> electrostatic fields steady currenis —» magnclosiatic fields time-varying currenis ••» electromagnetic fields (or wavesj Our aim in this chapter is to lay a firm foundation for our subsequent studies. This will involve introducing two major concepts: (1) electromotive force based on Faraday's ex- periments, and (2) displacement current, which resulted from Maxwell's hypothesis. As a result of these concepts, Maxwell's equations as presented in Section 7.6 and the boundary 369
370 Maxwell's Equations (a) (b) (0 Figure 9.1 Various types of time-varying current: (a) sinusoidal, (b) rectangular, (c) triangular. conditions for static EM fields will be modified to account for the time variation of the fields. It should be stressed that Maxwell's equations summarize the laws of electromag- netism and shall be the basis of our discussions in the remaining part of the text. For this reason, Section 9.5 should be regarded as the heart of this text.

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