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Richard G. Carter Electromagnetism for Electronic Engineers Download free ebooks at bookboon.com 2 Electromagnetism for Electronic Engineers © 2010 Richard G. Carter & Ventus Publishing ApS ISBN 978-87-7681-465-6 Disclaimer: The texts of the advertisements are the sole responsibility of Ventus Publishing, no endorsement of them by the author is either stated or implied. Download free ebooks at bookboon.com 3 Contents Electromagnetism for Electronic Engineers Contents Preface 8 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 Electrostatics in free space The inverse square law of force between two electric charges The electric field Gauss’ theorem The differential form of Gauss’ theorem Electrostatic potential Calculation of potential in simple cases Calculation of the electric field from the potential Conducting materials in electrostatic fields The method of images Laplace’s and Poisson’s equations The finite difference method Summary 10 10 11 13 16 18 20 21 24 26 27 29 31 2. 2.1 2.2 2.3 2.4 2.5 Dielectric materials and capacitance Insulating materials in electric fields Solution of problems involving dielectric materials Boundary conditions Capacitance Electrostatic screening 32 32 35 36 38 39 Please click the advert The next step for top-performing graduates Masters in Management Designed for high-achieving graduates across all disciplines, London Business School’s Masters in Management provides specific and tangible foundations for a successful career in business. 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For more information visit www.london.edu/mm, email mim@london.edu or give us a call on +44 (0)20 7000 7573. * Figures taken from London Business School’s Masters in Management 2010 employment report Download free ebooks at bookboon.com 4 Contents Electromagnetism for Electronic Engineers 2.6 2.7 2.8 2.9 2.10 2.11 Calculation of capacitance Energy storage in the electric field Calculation of capacitance by energy methods Finite element method Boundary element method Summary 42 43 45 45 47 47 3. 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Steady electric currents Conduction of electricity Ohmic heating The distribution of current density in conductors Electric fields in the presence of currents Electromotive force Calculation of resistance Calculation of resistance by energy methods Summary 48 49 50 52 54 55 56 58 58 4. 4.1 4.2 4.3 4.4 4.5 4.6 The magnetic effects of electric currents The law of force between two moving charges Magnetic flux density The magnetic circuit law Magnetic scalar potential Forces on current-carrying conductors Summary 59 59 61 64 65 67 67 Please click the advert Teach with the Best. Learn with the Best. Agilent offers a wide variety of affordable, industry-leading electronic test equipment as well as knowledge-rich, on-line resources —for professors and students. We have 100’s of comprehensive web-based teaching tools, lab experiments, application notes, brochures, DVDs/ CDs, posters, and more. See what Agilent can do for you. www.agilent.com/find/EDUstudents www.agilent.com/find/EDUeducators © Agilent Technologies, Inc. 2012 u.s. 1-800-829-4444 canada: 1-877-894-4414 Download free ebooks at bookboon.com 5 Contents Electromagnetism for Electronic Engineers 5. 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 The magnetic effects of iron Introduction Ferromagnetic materials Boundary conditions Flux conduction and magnetic screening Magnetic circuits Fringing and leakage Hysteresis Solution of problems in which μ cannot be regarded as constant Permanent magnets Using permanent magnets efficiently Summary 68 68 69 73 74 76 78 80 83 85 86 88 6. 6.1 6.2 6.3 Electromagnetic induction Introduction The current induced in a conductor moving through a steady magnetic field The current induced in a loop of wire moving through a non-uniform magnetic field Faraday’s law of electromagnetic induction Inductance Electromagnetic interference Calculation of inductance Energy storage in the magnetic field Calculation of inductance by energy methods The LCRZ analogy 89 89 90 Please click the advert 92 94 96 98 102 105 107 108 You’re full of energy and ideas. 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Wherever you are in your academic career, make your future a part of ours by visiting www.ubs.com/graduates. www.ubs.com/graduates Download free ebooks at bookboon.com 6 Contents Electromagnetism for Electronic Engineers 6.11 6.12 6.13 6.14 6.15 Energy storage in iron Hysteresis loss Eddy currents Real electronic components Summary 110 113 114 116 116 7. 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 Transmission lines Introduction The circuit theory of transmission lines Representation of waves using complex numbers Characteristic impedance Reflection of waves at the end of a line Pulses on transmission lines Reflection of pulses at the end of a line Transformation of impedance along a transmission line The coaxial line The electric and magnetic fields in a coaxial line Power flow in a coaxial line Summary 117 117 118 122 123 124 128 129 132 135 137 138 140 8. 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.9 Maxwell’s equations and electromagnetic waves Introduction Maxwell’s form of the magnetic circuit law The differential form of the magnetic circuit law The differential form of Faraday’s law Maxwell’s equations Plane electromagnetic waves in free space Power flow in an electromagnetic wave Summary 142 142 142 144 147 148 150 153 154 Bibliography 155 Appendix 157 Download free ebooks at bookboon.com 7 Preface Electromagnetism for Electronic Engineers Preface Electromagnetism is fundamental to the whole of electrical and electronic engineering. It provides the basis for understanding the uses of electricity and for the design of the whole spectrum of devices from the largest turbo-alternators to the smallest microcircuits. This subject is a vital part of the education of electronic engineers. Without it they are limited to understanding electronic circuits in terms of the idealizations of circuit theory. The book is, first and foremost, about electromagnetism, and any book which covers this subject must deal with its various laws. But you can choose different ways of entering its description and still, in the end, cover the same ground. I have chosen a conventional sequence of presentation, beginning with electrostatics, then moving to current electricity, the magnetic effects of currents, electromagnetic induction and electromagnetic waves. This seems to me to be the most logical approach. Authors differ in the significance they ascribe to the four field vectors E, D, B and H. I find it simplest to regard E and B as ‘physical’ quantities because they are directly related to forces on electric charges, and D and H as useful inventions which make it easier to solve problems involving material media. For this reason the introduction of D and H is deferred until the points at which they are needed for this purpose. Secondly, this is a book for those whose main interest is in electronics. The restricted space available meant that decisions had to be taken about what to include or omit. Where topics, such as the force on a charged particle moving in vacuum or an iron surface in a magnetic field, have been omitted, it is because they are of marginal importance for most electronic engineers. I have also omitted the chapter on radio-frequency interference which appeared in the second edition despite its practical importance. Thirdly, I have written a book for engineers. On the whole engineers take the laws of physics as given. Their task is to apply them to the practical problems they meet in their work. For this reason I have chosen to introduce the laws with demonstrations of plausibility rather than formal proofs. It seems to me that engineers understand things best from practical examples rather than abstract mathematics. I have found from experience that few textbooks on electromagnetism are much help when it comes to applying the subject, so here I have tried to make good that deficiency both by emphasizing the strategies of problem-solving and the range of techniques available. A companion volume is planned to provide worked examples. Most university engineering students already have some familiarity with the fundamentals of electricity and magnetism from their school physics courses. This book is designed to build on that foundation by providing a systematic treatment of a subject which may previously have been encountered as a set of experimental phenomena with no clear links between them. Those who have not studied the subject before, or who feel a need to revise the basic ideas, should consult the elementary texts listed in the Bibliography. Download free ebooks at bookboon.com 8 Preface Electromagnetism for Electronic Engineers The mathematical techniques used in this book are all covered either at A-level or during the first year at university. They include calculus, coordinate geometry and vector algebra, including the use of dot and cross products. Vector notation makes it possible to state the laws of electromagnetism in concise general forms. This advantage seems to me to outweigh the possible disadvantage of its relative unfamiliarity. I have introduced the notation of vector calculus in order to provide students with a basis for understanding more advanced texts which deal with electromagnetic waves. No attempt is made here to apply the methods of vector calculus because the emphasis is on practical problem-solving and acquiring insight and not on the application of advanced mathematics. I am indebted for my understanding of this subject to many people, teachers, authors and colleagues, but I feel a particular debt to my father who taught me the value of thinking about problems ‘from first principles’. His own book, The Electromagnetic Field in its Engineering Aspects (2nd edn, Longman, 1967) is a much more profound treatment than I have been able to attempt, and is well worth consulting. I should like to record my gratitude to my editors, Professors Bloodworth and Dorey, of the white and red roses, to Tony Compton and my colleague David Bradley, all of whom read the draft of the first edition and offered many helpful suggestions. I am also indebted to Professor Freeman of Imperial College and Professor Sykulski of the University of Southampton for pointing out mistakes in my discussion of energy methods in the first edition. Finally, I now realize why authors acknowledge the support and forbearance of their wives and families through the months of burning the midnight oil, and I am most happy to acknowledge my debt there also. Richard Carter Lancaster 2009 Download free ebooks at bookboon.com 9 1. Electrostatics in free space Electromagnetism for Electronic Engineers 1. Electrostatics in free space Objectives x x x x x x x x x x To show how the idea of the electric field is based on the inverse square law of force between two electric charges. To explain the principle of superposition and the circumstances in which it can be applied. To explain the concept of the flux of an electric field. To introduce Gauss’ theorem and to show how it can be applied to those cases where the symmetry of the problem makes it possible. To derive the differential form of Gauss’ theorem. To introduce the concept of electrostatic potential difference and to show how to calculate it from a given electric field distribution. To explain the idea of the gradient of the potential and to show how it can be used to calculate the electric field from a given potential distribution. To show how simple problems involving electrodes with applied potentials can be solved using Gauss’ theorem, the principle of superposition and the method of images. To introduce the Laplace and Poisson equations. To show how the finite difference method can be used to find the solution to Laplace’s equation for simple two-dimensional problems. 1.1 The inverse square law of force between two electric charges The idea that electric charges exert forces on each other needs no introduction to anyone who has ever drawn a comb through his or her hair and used it to pick up small pieces of paper. The existence of electric charges and of the forces between them underlies every kind of electrical or electronic device. For the present we shall concentrate on the forces between charges which are at rest and on the force exerted on a moving charge by other charges which are at rest. The question of the forces between moving charges, which is a little more difficult, is dealt with in Chapter 4. The science of phenomena involving stationary electric charges, known as electrostatics, finds many applications in electronics, including the calculation of capacitance and the theory of every type of active electronic device. Electrostatic phenomena are put to work in electrostatic copiers and paint sprays. They can also be a considerable nuisance, leading to explosions in oil tankers and the need for special precautions when handling metal-oxide semiconductor integrated circuits. The starting point for the discussion of electrostatics is the experimentally determined law of force between two concentrated charges. This law, first established by Coulomb (1785), is that the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. In the shorthand of mathematics the law may be written Download free ebooks at bookboon.com 10