* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Introduction - University of Illinois at Urbana
Magnetochemistry wikipedia , lookup
Scanning SQUID microscope wikipedia , lookup
Eddy current wikipedia , lookup
Superconductivity wikipedia , lookup
Electromagnetic compatibility wikipedia , lookup
History of electrochemistry wikipedia , lookup
Magnetoreception wikipedia , lookup
Multiferroics wikipedia , lookup
Electrostatics wikipedia , lookup
Computer science wikipedia , lookup
Electricity wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Magnetic monopole wikipedia , lookup
Magnetohydrodynamics wikipedia , lookup
Electromagnetic radiation wikipedia , lookup
Faraday paradox wikipedia , lookup
James Clerk Maxwell wikipedia , lookup
Lorentz force wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Electrical engineering wikipedia , lookup
Electronic engineering wikipedia , lookup
Electromagnetic field wikipedia , lookup
Maxwell's equations wikipedia , lookup
Electromagnetism wikipedia , lookup
Mathematical descriptions of the electromagnetic field wikipedia , lookup
Fundamentals of Electromagnetics: A Two-Week, 8-Day, Intensive Course for Training Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments by Nannapaneni Narayana Rao Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, India Amrita Viswa Vidya Peetham, Coimbatore August 11, 12, 13, 14, 18, 19, 20, and 21, 2008 Education is the manifestation of perfection already in man – Swami Vivekananda 1 Education is not the amount of information that is put into your brain and runs riot there, undigested all your life. We must have life-building, man-making, character-making assimilation of ideas. If you have assimilated five ideas and made them your life and character, you have more education than any man who has got by heart the whole library – Swami Vivekananda 2 Edward C. Jordan, Electromagnetic Personailty; Father of the ECE Department Edward C. Jordan was born in Edmonton, Alberta, Canada, on December 31, 1910. He received the BS degree in 1934 and MS degree in 1936 from the University of Alberta, and the PhD degree at The Ohio State University in 1940. In 1945, he followed his mentor, William L. Everitt, to the University of Illinois. At the University of Illinois, Dr. Jordan served as associate professor from 1945 to 1947, professor from 1947 to 1979, and as Head of the Department of Electrical Engineering, in which capacity he served for 25 years from 1954 until his retirement in 1979. His popular textbook, Electromagnetic Waves and Radiating Systems, was first published in 1950 by Prentice-Hall. A second edition, co-authored with K.G. Blamain, was published in 1968. 3 William L. Everitt Laboratory, Temple of Electrical and Computer Engineering 4 Some of the 136 full-time staff members of the EE Department in 1975 5 Amma Mata Amritanandamayi Devi, Chancellor, Amrita Vishwa Vidyapeetham “Fill your heart with love and express it in everything you do.” – Amma Mata Amritanandamayi Devi, Chancellor, Amrita Vishwa Vidyapeetham To students all over the world, I offer to you this book on Electromagnetics, the “Mother of Electrical and Computer Engineering,” with the spirit of the above message from Amma, the “Mother of Compassion!” 7 Amrita Vishwa Vidyapeetham, Ettimadai, Coimbatore 8 America, China, and India First, a Fascinating Story in the context of belief in the power of education – transcending the boundaries of national origin, race, and religion – to assure the future of the world 9 America, China, and India On April 18, 2006, while I was staying in the Le Meridien Hotel in New Delhi on one of my trips to the motherland, along with my wife, I received an email from one of my former colleagues at UIUC and an emeritus faculty member, on some department business. Along with it, he forwarded an e-mail from Da Hsuan Feng, then Vice President for Research and Economic Development and Professor of Physics at the University of Texas at Dallas, and now Senior Executive Vice President at National Chung Kung University in Tainan, Taiwan. Da Hsuan Feng was born in New Delhi in 1945 to Chinese parents, when his father, Paul Kuo-Jin Feng, was stationed as a foreign correspondent. 10 America, China, and India Paul Kuo-Jin Feng died tragically when Da Hsuan Feng was a young boy so that he knew little about what his father did, according to him. On the afternoon of April 18, 2006, it suddenly occurred to him that it might be interesting to google "Paul Feng." And he did just that and the results absolutely astounded him! It returned two websites, both of which were the same. What came to him on his screen stunned him so much that for a moment he was almost paralyzed! 11 America, China, and India From an article, “Forging an Asian identity,” by Manoj Das in The Hindu of January 7, 2001, he read the following: Speaking to Mr. Paul Feng of the Central News Agency on January 20, 1946, Pundit Jawaharlal Nehru, the first Prime Minister of India, said, “If China and India hold together, the future of Asia is assured.” This holding together need not be confined to diplomacy; it can, by all means, be a psychological force that can work wonders in the realms of creativity... 12 America, China, and India Da Hsuan Feng was stunned that 60 years ago then, his father was THE person who heard the profound statement — “If China and India hold together, the future of Asia is assured” — from Pundit Nehru. I was in high school in 1946, and from 1947, when I joined college in Madras, until I left India for the United States, I had several occasions to see the revered Prime Minister. Since I received the e-mail when I was in India in New Delhi in a hotel in a room overlooking the Parliament building and the Presidential mansion, where I met President Kalam three times in the preceding five months, the statement felt even more profound to me. 13 America, China, and India As I responded to my colleague with a copy to Da Hsuan Feng on April 20, 2006, just before my departure back to the United States after a very successful trip, from New Delhi: “Now, 60 years after that, that statement is even more significant. I would go further and say, with utmost reverence to Pundit Nehru, that today, if America, China, and India hold together, the future of the world is assured. In no other sphere of endeavor is the ‘holding together’ more important than in the sphere of education, because that is where future leaders are cultivated. It is in this regard that UIUC comes into the picture. And the reason I am here in India is on the matter of developing relations in India....” 14 America, China, and India It is my hope that this book (Fundamentals of Electromagnetics for Engineering) and its original U.S. edition and its international versions serve as a contribution, however small, in this regard by propagating the knowledge on the fundamentals of electromagnetics to students and academics throughout the world, transcending the boundaries of national origin, race, and religion. 15 Introduction to the Course 16 Goals of the Course Electromagnetics (also known under the terms, “electromagnetic theory,” “electricity and magnetism,” “electric and magnetic fields,” “electromagnetic fields,” “electromagnetic fields and waves,” and so on) is fundamental to the study of electrical (including electronics and communication) and computer engineering. The course goals are to impart the essential elements of engineering electromagnetics that (a) constitute the foundation for preparing electrical-related majors to take follow-on courses, and (b) represent the essentials for computer-related majors taking this course only. 17 Topical Coverage 1. Review of vector algebra and field concepts; sinusoidally time-varying fields and polarization 2. Line and surface integrals; Maxwell’ equations in integral form in free space 3. Maxwell’ equations in differential form in free space; curl and divergence 4. Uniform plane waves in free space 5. Materials and uniform plane waves; boundary conditions 6. Static fields, quasistatic fields, and development of transmission-line concept 7. Transmission lines; frequency-domain analysis, including Smith chart; time-domain analysis 8. Other topics 18 Textbooks U.S. and International Editions: “Fundamentals of Electromagnetics for Electrical and Computer Engineering,” Pearson Prentice Hall, 2009 (Published in May 2008) “Elements of Engineering Electromagnetics, Sixth Edition,”, Pearson Prentice Hall, 2004 Indian Editions: “Fundamentals of Elecromagnetics for Engineering,” LPE Indian Edition, Pearson Education, 2009 (Published in August 2008) “Elements of Engineering Electromagnetics, Sixth Edition,”, LPE Indian Edition, Pearson Education, 2006 19 Copies of Indian Editions, “Elements of Engineering Electromagnetics, Sixth Edition,” and “Fundamentals of Electromagnetics for Engineering,” for the Faculty Training Program at Amrita University from August 11, 2008 to August 21, 2008 Ultimate outcome of the course Maxwell’s Equations are the greatest equations, ever, as you will see later. They are the basis for the electromagnetic technologies that have brought this electronic age for the benefit of the humankind. By the end of the course, you will gain a fundamental understanding of these equations, and you will develop an appreciation for these equations. 21 Terminology Because I will be using the term “electrical and computer engineering” it is of interest to elaborate upon this terminology. In engineering departments in the United States educational institutions, electrical and computer engineering is generally one academic department, although not in all institutions. The name, ECEDHA, Electrical and Computer Engineering Department Heads Association, reflects this situation. In the College of Engineering at the University of Illinois at Urbana-Champaign (UIUC), the Department of Electrical and Computer Engineering (ECE) offers two undergraduate programs leading to the Bachelor of Science degrees: Electrical Engineering and Computer Engineering. 22 The Scope of Electrical Engineering “A list of the twenty greatest engineering achievements of the twentieth century compiled by the National Academy of Engineering includes ten achievements primarily related to the field of electrical engineering: electrification, electronics, radio and television, computers, telephone, internet, imaging, household appliances, health technologies, and laser and fiber optics. The remaining achievements in the list - automobile, airplane, water supply and distribution, agricultural mechanization, air conditioning and refrigeration, highways, spacecraft, petroleum/petrochemical technologies, nuclear technologies, and high-performance materials - also require knowledge of electrical engineering to differing degrees. In the twenty-first century the discipline of electrical engineering continues to be one of the primary drivers of change and progress in technology and standards of living around the globe.” 23 NAE’s List of Greatest Engineering Achievements of the 20th Century • • • • • • • • • • Electrification Automobile Airplane Water Supply & Distribution Electronics Radio & Television Agricultural Mechanization Computers Telephone Air Conditioning & Refrigeration Red indicates areas where ECE at UIUC has had influence. • • • • • • • Highways Spacecraft Internet Imaging Household Appliances Health Technologies Petroleum/Petrochemical Technologies • Laser & Fiber Optics • Nuclear Technologies • High-Performance Materials 24 The Scope of Computer Engineering “Computer engineering is a discipline that applies principles of physics and mathematics to the design, implementation, and analysis of computer and communication systems. The discipline is broad, spanning topics as diverse as radio communications, coding and encryption, computer architecture, testing and analysis of computer and communication systems, vision, and robotics. A defining characteristic of the discipline is its grounding in physical aspects of computer and communication systems. Computer engineering concerns itself with development of devices that exploit physical phenomena to store and process information, with the design of hardware that incorporates such devices, and with software that takes advantage of this hardware's characteristics. It addresses problems in design, testing, and evaluation of system properties, such as reliability, and security. It is an exciting area to work in, one that has immediate impact on the 25 technology that shapes society today.” The Illinois Curriculum in Electrical Engineering For the electrical engineering program at Illinois, the core curriculum focuses on fundamental electrical engineering knowledge: circuits, systems, electromagnetics, solid state electronics, computer engineering, and design. A rich set of elective courses permits students to select from collections of courses in seven areas of electrical and computer engineering: bioengineering, acoustics, and magnetic resonance engineering; circuits and signal processing; communication and control; computer engineering; electromagnetics, optics, and remote sensing; microelectronics and quantum electronics; power and energy systems. 26 The Illinois Curriculum in Computer Engineering For the computer engineering program, the core curriculum focuses on fundamental computer engineering knowledge: circuits, systems, electromagnetics, computer engineering, solid state electronics, and computer science. A rich set of elective courses permits students to concentrate in any sub-discipline of computer engineering including: computer systems; electronic circuits; networks; engineering applications; software, languages, and theory; and algorithms and mathematical tools. 27 Electromagnetics, the “Mahatmyam (Greatness)”of Maxwell’s equations, and the Teaching of Electromagnetics 28 29 30 So, why are these poor little guys so perplexed at the sight of equations which “God said”? 31 The inscription that you saw on the first slide is from a T-shirt (or undershirt), which I purchased some years ago in the MIT bookstore in Cambridge, Massachusetts. The coffee cup on the second slide was distributed by the Electromagnetics Laboratory of the University of Illinois at Urbana-Champaign some years ago. There are probably other articles of similar nature. 32 Maxwell’s Equations The equations that you have seen are known as Maxwell’s equations, after James Clerk Maxwell (183179). I call them EMantras, because they form the basis for electromagnetics (EM), which is the science of interdependent electric and magnetic fields. 33 Einstein’s description of Maxwell’s work Albert Einstein described Maxwell’s discoveries as “the most profound and the most fruitful that physics has experienced since the time of Newton.” 34 The most significant event of the nineteenth century Physicist, Richard Feynman, noted: From a long view of the history of mankind – seen from, say, ten thousand years from now, – there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell’s theory of the laws of electrodynamics. 35 The greatest equations ever In 2004, PHYSICS WORLD magazine conducted a poll asking its readers to send their short lists of the greatest equations ever and also asked them to explain why their nominations belonged on the list and why, if at all, the topic matters. They received about 120 responses -- including single candidates as well as lists -- proposing about 50 different equations. They ranged from obvious classics to "overlooked" candidates, personal favorites and equations invented by the respondents themselves. The result was published under CRITICAL POINT in the October 6, 2004 issue. 36 The greatest equations ever The Result and Explanation: Maxwell’s equations of electromagnetism and the Euler equation top a poll to find the greatest equations of all time. The article said: Although Maxwell’s equations are relatively simple, they daringly recognize our perception of nature, unifying electricity and magnetism and linking geometry, topology and physics. They are essential to understanding the surrounding world. And as the first field equations, they not only showed scientists a new way of approaching physics but also took them on the first step towards the unification of the fundamental forces of nature. 37 Holonyak on Electromagnetics (EM) “… I am talking about the areas of science and learning that have been at the heart of what we know and what we do, that which has supported and guided us and which is fundamental to our thinking. It is electromagnetism (EM) in all its many forms that has been so basic, that haunts us and guides us…” – Nick Holonyak, Jr., John Bardeen Endowed Chair Professor of Electrical and Computer Engineering and of Physics, UIUC, and the inventor of the semiconductor visible LED, laser, quantum-well laser, and the transistor laser. 38 Presenting Book to Nick Holonyak, Jr., Inventor of the LED and the Transistor Laser 39 About John Bardeen On March 6, 2008, the United States Post Office issued stamps honoring four scientists, one of whom is John Bardeen, co-inventor of the transistor and two-time Nobel Prize winner in Physics, first time for transistor and second time for superconductivity. The unveiling of the stamp ceremony took place on the campus of the University of Illinois at Urbana-Champaign in Room 151 of the Loomis Laboratory of Physics, in Urbana. Bardeen was a professor of physics and of electrical and computer engineering. 40 NNR with John Bardeen Stamp 41 George Swenson on Electromagnetics “The electromagnetic theory, as we know it, is surely one of the supreme accomplishments of the human intellect, reason enough to study it. But its usefulness in science and engineering makes it an indispensable tool in virtually any area of technology or physical research.” – George W. Swenson, Jr., Professor Emeritus of Electrical and Computer Engineering, UIUC, and a pioneer in the field of radio-astronomy. 42 Radio telescopes designed and built by George W. Swenson Jr. at the University of Illinois. Left: 120-foot-diameter parabolic dish. Right: 400-foot-diameter parabolic cylinder fashioned out of a stream bed. 43 Electromagnetics is all around us! In simple terms, every time we turn a switch on for electrical power or for an electronic equipment, every time we press a key on our computer key board or on our cell phone, or every time we perform a similar action involving an everyday electrical device, electromagnetics comes into play. 44 Some modern applications of EM (Courtesy of Weng C. Chew) Biomedical Engineering & BioTech Wireless Comm. & Propagation RCS Analysis, Design, ATR & Stealth Technology Physics Based Signal Processing & Imaging Computer Chip Design & Circuits ELECTROMAGNETICS Antenna Analysis & Design EMC/EMI Analysis Lasers & Optoelectronics MEMS & Microwave Engineering Remote Sensing & Subsurface Sensing & NDE 45 Fundamental to the Study of ECE It is the foundation for the technologies of electrical and computer engineering, spanning the entire electromagnetic spectrum, from dc to light. As such, in the context of engineering education, it is fundamental to the study of electrical and computer engineering. 46 Foundation for the technologies of electrical and computer engineering 47 Fundamental to the Study of ECE In 1963, the American Institute of Electrical Engineers (AIEE) and the Institute of Radio Engineers (IRE) were merged into the Institute of Electrical and Electronics Engineers (IEEE), a global nonprofit organization with over 375,000 members, and “the world's leading professional association for the advancement of technology.” The IEEE logo or badge is a merger of the badges of the two parent organizations. It contains a vertical arrow surrounded by a circular arrow, within a kite-shaped border. No letters clutter the badge because a badge without letters can be read in any language. The AIEE badge had the kite shape which was meant to symbolize the kite from Benjamin Franklin’s famous kite experiment to study electricity. The IRE badge had the two arrows that symbolize the right hand rule of electromagnetism. 48 Fundamental to the Study of ECE Alternatively, the vertical arrow can be thought of as representing one of the two fields, electric or magnetic, and the circular arrow surrounding it representing the second field, produced by it, so that together they represent an electromagnetic field. 49 Fundamental to the Study of ECE Whether this logo of IEEE was intended to be a recognition of the fact that electromagnetics is fundamental to all of electrical and computer engineering, it is a fact that all electrical phenomena are governed by the laws of electromagnetics, and hence, the study of electromagnetics is essential to all branches of electrical and computer engineering, and indirectly impacts many other branches. 50 EM is so fundamental that even Mac “Circuits” Van Valkenburg was caught having fun “communicating” the RH Rule to Robert “Communications” Lucky! Wonderful picture! An amusing incident One of the earliest postwar programs to be established at UIUC was a program in radio direction finding (RDF). It was intended as a basic research program, sponsored by the Office of Naval Research. When the sponsor was asked by the research supervisor, Edward Jordan, what facets of the field might be of particular interest, the answer received was: “Look, you know Maxwell’s equations, the Russians know Maxwell’s equations; you take it from there.” Jordan was amused that it would be difficult to get more basic than that. 52 Wullenweber Array at Bondville Road Field Station of the RDF Laboratory • • • • Used in Radio Direction Finding Laboratory In operation 1955-1980 Used 120 antennas and was 1000 ft in diameter Operated in frequency range of 4-16 MHz 53 Wullenweber array of the RDF Laboratory (1955 – 1980) 54 Discovering Wullenweber while riding the Pineapple Express at the Dole Plantation on the island of Oahu, Hawaii, with family on June 4, 2005, as a reminder 55 Wullenweber and Bananas (My favorite slide) 56 So, what is Electromagnetics? By the very nature of the word, electromagnetics implies having to do with a phenomenon involving both electric and magnetic fields and furthermore coupled. This is indeed the case when the situation is dynamic, that is, time-varying, because time-varying electric and magnetic fields are interdependent, with one field producing the other. 57 What is Electromagnetics? In other words, a time-varying electric field or a time-varying magnetic field cannot exist alone; the two fields coexist in time and space, with the space-variation of one field governed by the time-variation of the second field. This is the essence of Faraday’s law and Ampere’s circuital law, the first two of the four Maxwell’s equations resulting in wave propagation. 58 About Electromagnetics (Continued) Only when the fields are not changing with time, that is, for the static case, they are independent; a static electric field or a static magnetic field can exist alone, with the exception of one case in which there is a one-way coupling, electric field resulting in magnetic field, but not the other way. 59 About Electromagnetics (Continued) Thus, in the entire frequency spectrum, except for dc, all electrical phenomena are, in the strictest sense, governed by interdependent electric and magnetic fields, or electromagnetic fields. Statics Dynamics dc Frequency, f Light 60 Quasistatic Approximation However, at low frequencies, an approximation, known as the “qusistatic approximation,” can be made in which the time-varying fields in a physical structure are approximated to have the same spatial variations as the static fields in the structure obtained by setting the source frequency equal to zero. 61 Quasistatic Approximation (Continued) Thus, although the actual situation in the structure is one of electromagnetic wave nature, it is approximated by a dynamic but not wavelike nature. As the frequency becomes higher and higher, this approximation violates the actual situation more and more, and it becomes increasingly necessary to consider the wave solution. 62 Statics Quasistatics Dynamics dc Frequency, f Light Statics: f = 0; t 0; dc Dynamics: No restriction; complete Maxwell’s equations; Electromagnetic waves Quasistatics: Low-frequency extension of statics, or low-frequency approximation of dynamics; l 2 63 Maxwell’s Equations are elegant and beautiful. As profound as they are, they are actually quite simple to explain and understand. 64 Maxwell’s Equations d E dl – B dS C dt S Electric field intensity V m S C m3 Wb m2 A m Current density A m2 V r dv Charge density Magnetic flux density d H dl J dS D dS + C S dt S Magnetic field intensity D dS S B dS 0 Displacement flux density C m2 65 Faraday’s Law, the first EMantra d C E • dl – dt S B • dS B S C dS Electromotive Force (emf) or voltage around C = Negative of the time rate of increase of the magnetic flux crossing S bounded by C. 66 C E • dl = Voltage around C, also known as electromotive force (emf) around C (but not really a force), V m m, or V. S B • dS = Magnetic flux crossing S, Wb m2 m2 , or Wb. d – S B • dS = Time rate of decrease of dt magnetic flux crossing S, Wb s, or V. 67 Ampere’s Circuital Law, the second EMantra d C H • dl S J • dS + dt S D • dS J, D S C dS Magnetomotive force (mmf) around C = Current due to flow of charges crossing S bounded by C + Time rate of increase of electric (or displacement) flux crossing S 68 C H • dl = Magnetomotive force (only by analogy with electromotive force), A m m, or A. S J • dS = Current due to flow of charges crossing S, Amp m2 m2 , or A. S D • dS = Displacement flux, or electric flux, crossing S, 2 2 C m m , or C. 69 d D • dS = Time rate of increase of S dt displacement flux crossing S, or, displacement current crossing S, C s, or A. 70 Gauss’ Law for the Electric Field, the third EMantra C 3 D d S r dv m , or C 3 S V m D r • V S dS Displacement flux emanating from a closed surface S = charge contained in the volume V bounded by S = charge enclosed by S 71 Gauss’ Law for the Magnetic Field, the fourth EMantra S B • dS = 0 B dS S Magnetic flux emanating from a closed surface S = 0. 72 Out of the four EMantras, only the first two, Faraday’s and Ampere’s circuital laws are independent. The fourth Mantra, Gauss’ law for the magnetic field, follows from Faraday’s law, and the third Mantra, Gauss’ law for the electric field, follows from Ampere’s circuital law, with the aid of an auxiliary equation, the law of conservation of charge. 73 Law of Conservation of Charge, an auxiliary EMantra S J • dS + d r dv 0 V dt r(t) V S J dS Current due to flow of charges emanating from a closed surface S = Time rate of decrease of charge enclosed by S. 74 Maxwell’s Equations in Differential Form and the Continuity Equation B xE= – t D x H J+ t Faraday’s Law Ampere’s Circuital Law D r Gauss’ Law for the Electric Field B 0 Gauss’ Law for the Magnetic Field r J + 0 t Continuity Equation 75 Ez Ey Bx – – y z t By Ex Ez – – z x t E y E x Bz – – x y t Lateral space derivatives of the components of E Time derivatives of the components of B Dx Dy Dz + + r x y z Longitudinal derivatives of the components of D Charge density 76 The “Mahatmyam (Greatness)” of Maxwell’s Equations d C E • dl = – dt S B • dS d C H • dl = S J • dS + dt S D • dS 77 The “Mahatmyam (Greatness)” of Maxwell’s Equations + J + Law of Conservation of Charge r Gauss’ Law for E Ampere’s Circuital Law H ,B Faraday’s Law D,E 78 The “Mahatmyam (Greatness)” of Maxwell’s Equations Thus, Faraday's law says that a time-varying magnetic field gives rise to an electric field, the space-variation of which is related to the time-variation of the magnetic field. Ampere's circuital law tells us that a time-varying electric field produces a magnetic field, the space variation of which is related to the time-variation of the electric field. Thus, if one time-varying field is generated, it produces the second one, which in turn gives rise to the first one, and so on, which is the phenomenon of electromagnetic wave propagation, characterized by time delay of propagation of signals. In addition, Ampere’s circuital law tells us that an electric current produces a magnetic field, so that a time-varying current source results in a time-varying magnetic field, beginning the process of one field generating the second. 79 Hertzian Dipole I(t) I(t) H(t) E(t) 80 Radiation from Hertzian Dipole 81 Hertzian dipole and radiation pattern on the covers of the U.S. and Indian Editions of “Fundamentals of Electromagnetics” The Contribution of Maxwell You will have noted that none of the four equations are named after Maxwell. So, the question arises as to why they are known as Maxwell’s equations. It is because of a purely mathematical contribution of Maxwell. This mathematical contribution is the second term on the right side of Ampere’s circuital law. Prior to that, Ampere’s circuital law consisted of only the first term on the right side. 83 The Contribution of Maxwell Without the second term on the right side of Ampere’s circuital law, the loop is not complete and hence there is no interdependence of timevarying electric and magnetic fields and no EM waves! d C E • dl = – dt S B • dS d C H • dl = S J • dS + dt S D • dS 84 Unifying Electricity and Magnetism Thus, the purely mathematical contribution of Maxwell in 1864 unified electricity and magnetism and predicted the generation of EM waves owing to the interdependence of time-varying electric and magnetic fields. Only 23 years later in 1887, eight years after his death in 1789, the theory was proved correct by the experimental discovery of EM waves by Heinrich Hertz. 85 Parallel with Principles from Upanishads In fact, Maxwell’s Equations are as fundamental to the science of all electrical phenomena and hence to modern living as the Guiding Principles, from the Taittriyopanishad are to spirituality. 86 The Guiding Principles from Upanishads 87 The Guiding Equations of Electromagnetics 88 Maxwell’s Equations parallel to the Principles in Upanishads! Isn’t it fascinating! 89 So, why are these poor little guys so perplexed at the sight of Maxwell’s Equations? 90 Why is the teaching and learning of EM so dreaded, as implied by this mnemonic? HOW I WANT A DRINK, 3. 1 4 1 5 ALCOHOLIC, OF COURSE, 9 2 6 AFTER THE HEAVY LECTURES 5 3 5 8 INVOLVING ELECTRO-MAGNETICS! 9 7 9 91 Incomplete list of reasons given • Abstract (not practical; ideal; theoretical; hard to understand; difficult; abstruse) • Mathematical complexity • Vector notation • Curl, divergence, and gradient • Highly conceptual 92 The approach to the teaching of electromagnetics While these might be valid reasons to differing degrees for different people, depending on their background preparations, let us look at the teaching of EM. 93 The approach to the teaching of electromagnetics Historically, the development of major technologies based on Maxwell’s equations occurred in the sequence of electrically and magnetically based technologies (electromechanics and electrical power) in the nineteenth century; electronics hardware and software in the twentieth century; and photonics technologies, entering into the twenty-first century. 94 Progression of technologies based on Maxwell’s Equations 95 The approach to the teaching of electromagnetics The teaching of electromagnetics evolved following this sequence, that is, beginning with a course on electrostatics, magnetostatics, energy and forces, and in some cases quasistatic fields, followed by Maxwell’s equations for time-varying fields and an introduction to electromagnetic waves. This course was then followed by one or more courses on transmission lines, electromagnetic waves, waveguides and antennas. 96 The historical, or, “inductive” approach The teaching of the introductory course in this manner is known as the “inductive” approach, that is, an approach consisting of developing general principles from particular facts, which in this case was developing complete set of Maxwell’s equations from the particular laws of static fields. Since generally much time is taken up for the coverage of static fields before getting to the complete set of Maxwell’s equations, the time is cut short (and in some cases not available) for the more interesting and useful material, centered on electromagnetic waves. This is the principal drawback of the traditional, inductive, approach, which is unnecessarily aggravating, because all the mathematics and concepts taught in the context of static fields can not only be taught but taught better and with less aggravation with time-varying fields. 97 The “Deductive” Approach In contrast to the “inductive” approach is the “deductive” approach, that is, an approach in which one begins with the general principles that are accepted as true and then applies it to particular cases, which in this case is beginning with the complete set of Maxwell’s equations for time-varying fields and then developing their applications, as well as considering special cases of static and quasistatic fields. This approach permits the structuring of the course so that (a) it constitutes the foundation for students taking follow-on courses, as well as (b) imparting the essentials for students taking this course only in EM. 98 “Deduction” versus “Induction” Deduction applies to the process in which one starts with a general principle that is accepted as true and applies it to a particular case, arrives at a conclusion that is true if the starting principle was true, as in All animals die; this is an animal; therefore this will die. Induction applies to the process by which one collects many particular cases, finds out by experiment what is common to all of them, and forms a general rule or principle which is probably true, as in Every animal I have tested died; probably all animals die. 99 The “Deductive” Approach (Continued) Since the deductive approach begins with the complete Maxwell’s equations, it provides an appreciation of the fact that regardless of how low the frequency is, as long as it is nonzero, the phenomenon is one of electromagnetic waves, resulting from the interdependence of time-varying electric and magnetic fields. Then, statics and quasistatics are treated as special cases. 100 The “Deductive” Approach (Continued) Furthermore, combining the deductive approach with the thread of statics-quasistatics-waves makes it quite clear that, along the frequency spectrum, the quasistatic behavior approached from the static (zero frequency) limit as an extension of the static behavior to dynamic behavior of first order in frequency is the same as the low-frequency behavior approached from the other (higher frequencies) side, by approximating the exact dynamic solution for low frequencies. This very important concept is not always clearly understood or appreciated when the inductive approach is employed. Statics l 2 Quasistatics Dynamics dc Frequency, f Light 101 The approach to the teaching of electromagnetics And the deductive approach is the way of teaching Maxwell’s equations as “God said,” as contrasted with the inductive approach, which is the way in which they were evolved by human intellect. I am not a philosopher but it should not be difficult to accept that Maxwell and others did not create the equations; they only discovered what “God said” in the first place, through a series of ingenious steps over time! 102 Knowledge is inherent man; no knowledge comes from outside.… We say Newton discovered gravitation. Was it sitting anywhere in a corner waiting for him? It was in his own mind; the time came and he found it out. All knowledge that the world has ever received comes from the mind; the infinite library of the universe is in your own mind. The external world is simply the suggestion, the occasion, which sets you to study your own mnd – Swami Vivekananda 103 So, why is the teaching and learning of EM so dreaded? It is not entirely because of EM, but also because of the way it is taught! 104 PoEM on why study EM! To the students from all around the world And to the students all over the world EMpowered by the Jordan name And inspired by the AMRITA name I offer to you this book on EM Beginning with this poem which I call PoEM If you are wondering why you should study EM Let me tell you about it by means of this PoEM First you should know that the beauty of EM Lies in the nature of its compact formalism Through a set of four wonderful EMantras Familiarly known as Maxwell's equations They might be like mere four lines of mathematics to you But in them lie a wealth of phenomena that surround you Based on them are numerous devices That provide you everyday services Without the principles of Maxwell's equations Surely we would all have been in the dark ages Because there would be no such thing as electrical power Nor would there be electronic communication or computer Which are typical of the important applications of ECE And so you see, EM is fundamental to the study of ECE. 105 PoEM on why study EM! (Continued) So, you are curious about learning EM Let us proceed further with this PoEM First you should know that E means electric field And furthermore that B stands for magnetic field Now, the static E and B fields may be independent But the dynamic E and B fields are interdependent Causing them to be simultaneous And to coexist in any given space Which makes EM very illuminating And modern day life most interesting For it is the interdependence of E and B fields That is responsible for electromagnetic waves In your beginning courses you might have learnt circuit theory It is all an approximation of electromagnetic field theory So you see they put the cart before the horse But it is okay to do that and still make sense Because at low frequencies circuit approximations are fine But at high frequencies electromagnetic effects are prime So, whether you are an electrical engineer Or you happen to be a computer engineer Whether you are interested in high frequency electronics Or may be high-speed computer communication networks You see, electromagnetic effects are prime Studying the fundamentals of EM is sublime. 106 PoEM on why study EM! (Continued) If you still have a ProblEM with EM, Because it is full of abstract mathematics, I say, my dear ECE student who dislikes electromagnetics Because you complain it is full of abstract mathematics I want you to know that it is the power of mathematics That enabled Maxwell’s prediction through his equations Of the physical phenomenon of electromagnetic radiation Even before its finding by Hertz through experimentation In fact it was this accomplishment That partly resulted in the entitlement For the equations to be known after Maxwell Whereas in reality they are not his laws after all For example the first one among the four of them Is Faraday’s Law expressed in mathematical form You see, mathematics is a compact means For representing the underlying physics Therefore do not despair when you see mathematical derivations Throughout your textbook on the Fundamentals of Electromagnetics Instead look through the derivations to understand the concepts Realizing that mathematics is only a means to extend the physics Think of you as riding the horse of mathematics To conquer the new frontier of electromagnetics Let you and me together go on the ride As I take you through the steps in stride, with grattitude! 107 The End 108