Graphic on cover from Bellm. H.: "High-frequency characte ristics of impulse-voltage measuring systems considering the transient radiation field". Ph.D. thesis. Faculty of El. Engineering University of Karlsruhe.lg81 Adolf J. Schwab Field Theory Concepts Electromagnetic Fields Maxwell's Equations grad, curl, div etc. Finite-Element Method Finite-Difference Method Charge Simulation Method Monte Carlo Method With 49 Figures Springer-Verlag Berlin Heidelberg NewY ork London Paris Tokyo Prof. Dr.-Ing. Adolf Schwab Institut fUr Elektroenergiesysteme und Hochspannungstechnik Universitiit Karlsruhe Kaiserstr. 12 7500 Karlsruhe 1 ISBN-13: 978-3-642-48943-3 e-ISBN-13: 978-3-642-48941-9 001: 10.1007/978-3-642-48941-9 Library of Congress Cataloging-in-Publication Data Schwab, Adolf J. [Begriffswelt der Feldtheorie. English] Field theory concepts: electromagnetic fields. Maxwell's equations, grad, curl, div, etc. finite-element method, finite-difference method, charge simulation method, Monte Carlo method / Adolf J. Schwab. --[1st ed.] Rev. translation of the 2nd German ed. of: Begriffswelt der Feldtheorie. ISBN-13: 978-3-642-48943-3 I. Field theory (Physics) 2. Electromagnetic fields. 3. Maxwell equations. 4. Mathematical pyhsics. I. Title. QC173.7.S3813 1988 530.1'4--dc 19 88-24901 This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provision of the German Copyright Law of September9, 1965, in its version ofJ une 24, 1985,and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1988 Softcover reprint of the hardcover 1st edition 1988 The use ofr egistered names,trademarks,etc. in this publication does not imply,even in the absence ofa specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 216113020 543210 -Printed on acid-free paper No mathematical purist could ever do the work involved in Maxwell's treatise. He might have all the mathematics, and much more, but it would be to no purpose, as he could not put it together without the physical guidance. This is in no way to his discredit, but only illustrates different ways of thought. Oliver Heaviside Preface to the English Edition In translating his book Field Theory Concepts form the original German 2nd edition, published by Springer publishers in 1987, the author has added a number of revisions and late de velopments in the field. Thus, this translation represents es sentially a revised edition of the German text, adapted for American readers. Due to the different historical development of concepts in the United States and in Europe, the author anticipates occasional discussions on his pOints of view. The format of this book will likely seem unusual to many American readers. This is partially a product of different styles between the continents, and, in the author's opinion, is not al together bad. More importantly, however, the new format re presents a new approach to the teaching and understanding of electromagnetic field theory. An important example of this is the emphasis placed on the static, quasistatic, and dynamic nature of fields. In trying to present the most lucid explanation of some difficult concepts, the author has tried to use highly illustrative terms. In some cases, this may necesitate an extra effort on the part of the reader to translate, mentally, his preconceived notions into the author's conceptual language. No apology is made for this, as the author is confident that this effort will be richly re warded by a fuller understanding. VIII Regarding this Engish edition the author acknowledges his ap preciation to Prof. Dr. Roland Schinzinger. University of California. Irvine. Prof. Dr. Chathan Cooke. Massachussets Insti tute of Technology. and Prof. Dr. Peter L. Levin Worcester Poly technic Institute for numerous valuable suggestions and for thorough reading and polishing of the manuscript. Of course. any mistakes and omissions are ultimately my own. Karlsruhe, June, 1988 Prof. Dr. Adolf J. Schwab Preface Maxwell's equations constitute the theoretical basis for the en tire world of electrical and electronic engineering. Frequently, they appear only implicitly, for instance in control theory or in digital electronics; however, in electromagnetic compatibility, antenna theory, numerical calculation of electric and magnetic fields, electric energy systems, plasma phYSiCS, biocyb emetics , etc. there is no escape. Despite their importance, many students are not as familiar with these equations as would be desirable; for many an electrical engineer they remain a sealed book all their lives. Therefore, this booklet attempts to in troduce the reader gently on a step-by-step basis into field theory jargon and to present the essence of Maxwell's equations in a concise yet illustrative manner. In order to avoid that the reader "cannot see the forest for the trees," this unconventional introduction frequently quits where many established books on field theory elaborate; this is part of this booklet's appeal. Many years of teaching, research and development in several of the fields mentioned above have prompted the author to choose this presentation, which by no means is intended to replace proven textbooks, rather to lure students into reading those. It is assumed, however, that the reader has some familiarity with electricity and magnetism. Even very elementary terms, e.g. flUX, induction, displacement etc. make beginners feel lastingly uncomfortable. Therefore, x this text starts with a demonstration of obvious formal analogies of electric. magnetic and conduction field quantities. This is followed by a detailed interpretation of Maxwell's equations in integral form. The differential form of Maxwell's equations calls for a com prehensive explanation of the terms curl and div. which gen erally are conceptually demanding. The consistent use of the descriptive paired concepts vortex strength and vortex density for Circulation and rotation (curl). as well as of the paired concepts source strength and source density for the net flux through a closed surface and for the divergence. is regarded an innovative contribution to a thorough understanding of the relationship between global and local field quantities. Although. at frrst glance. those paired concepts may look strange to the reader they resemble the fundamental idea of a transparently structured electromagnetic field theory. The explanation of the terms gradient. potential. and potential jUnction is followed by the potential equations for electric fields with and without space charges. Likewise, the deduction of scalar and vector magnetic potentials is followed by the scalar and vector potential equations for magnetic fields. The discussion of scalar and vector potential concepts serves simul taneously as the first introduction of the inverse integral operators {curl}-l, {div}-l and {grad}-l which prove as helpful tools in finding the general solution of differential equations of several independent variables. When electric and magnetic fields are claSSified according to their time dependency. conSiderable emphasis is placed on an intimate understanding of the terms static, quasi-static and nonstattonary fields. and on the deduction of the wave equation. The easily understood transmission-line equations provide the basis for a systematic. distinct claSSification of terms such as telegraphist's equation. wave equation. dijJusion equation. Laplace equation. Helmholtz equation. and the renowned Schroedinger equation. This is followed by Lorentz's tnvariance of Maxwell's equations which demonstrates that the difference XI between electric and magnetic fields is not as marked as daily engineering problems would lead one to believe. Finally, the last chapter aquaints the reader with four different concepts of numerical field calculation - finite-element meth od, finite-difference method, charge simulation method and the Monte Carlo method. The author is grateful to former and present students A. and I. Brauch, R. Biiche, P. Deister, Th. Dunz, Dr. F. Imo, H. Kunz, R. Maier, B. Schaub, and Dr. H.H. Zimmer for their comments and proof reading. May thanks also extend to many anonymous reviewers who have inspired me to make changes in the second German edition. Special thanks go to Mrs. Therese Farber for her contributions during the translation, to Mrs. Madeleine Michels and Mrs. Gerdi Ottmar, appreciated typists of the camera-ready manu script, to our artist Mrs. Edith Miiller, and ultimately, to Dr. Julia Abrahams, Albrecht von Hagen, and Dr. Ludwig, Springer publishers, for their steady support and encouragement. Anyone fmding errors in the text or figures is kindly invited to write to the author for the benefit of the readers of a subse quent printing. Karlsruhe, June, 1988 Prof. Dr. Adolf J. Schwab High-Voltage Research Laboratory University of Karlsruhe 7500 Karlsruhe FR-Germany