chapter 01 - PART 1 VECTOR ANALYSIS Chapter 7 T V.S-f...

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PART 1 VECTOR ANALYSIS
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Chapter 7 T•,—••• ' ' V ' '.S-f » VECTOR ALGEBRA One thing I have learned in a long life: that all our science, measured against reality, is primitive and childlike—and yet is the most precious thing we have. —ALBERT EINSTEIN 1.1 INTRODUCTION Electromagnetics (EM) may be regarded as the study of the interactions between electric charges at rest and in motion. It entails the analysis, synthesis, physical interpretation, and application of electric and magnetic fields. Kkctioniiiniutics (k.Yli is a branch of physics or electrical engineering in which electric and magnetic phenomena are studied. EM principles find applications in various allied disciplines such as microwaves, an- tennas, electric machines, satellite communications, bioelectromagnetics, plasmas, nuclear research, fiber optics, electromagnetic interference and compatibility, electromechanical energy conversion, radar meteorology," and remote sensing. 1 ' 2 In physical medicine, for example, EM power, either in the form of shortwaves or microwaves, is used to heat deep tissues and to stimulate certain physiological responses in order to relieve certain patho- logical conditions. EM fields are used in induction heaters for melting, forging, annealing, surface hardening, and soldering operations. Dielectric heating equipment uses shortwaves to join or seal thin sheets of plastic materials. EM energy offers many new and exciting possibilities in agriculture. It is used, for example, to change vegetable taste by reducing acidity. EM devices include transformers, electric relays, radio/TV, telephone, electric motors, transmission lines, waveguides, antennas, optical fibers, radars, and lasers. The design of these devices requires thorough knowledge of the laws and principles of EM. For numerous applications of electrostatics, see J. M. Crowley, Fundamentals of Applied Electro- statics. New York: John Wiley & Sons, 1986. 2 For other areas of applications of EM, see, for example, D. Teplitz, ed., Electromagnetism: Paths to Research. New York: Plenum Press, 1982.
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4 Vector Algebra + 1.2 A PREVIEW OF THE BOOK The subject of electromagnetic phenomena in this book can be summarized in Maxwell's equations: V-D = p v (1.1) V B = 0 (1.2) • • * • • • *•- V X E = - (1.3) dt V X H = J + — (1.4) dt where V = the vector differential operator D = the electric flux density B = the magnetic flux density E = the electric field intensity H = the magnetic field intensity p v = the volume charge density and J = the current density. Maxwell based these equations on previously known results, both experimental and theo- retical. A quick look at these equations shows that we shall be dealing with vector quanti- ties. It is consequently logical that we spend some time in Part I examining the mathemat- ical tools required for this course. The derivation of eqs. (1.1) to (1.4) for time-invariant conditions and the physical significance of the quantities D, B, E, H, J and p v will be our aim in Parts II and III. In Part IV, we shall reexamine the equations for time-varying situa- tions and apply them in our study of practical EM devices.
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