Electromagnetic Field Theory: A Problem Solving Approach Part 2. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Notes to the Student and Instructor vii A NOTE TO THE STUDENT In this text I have tried to make it as simple as possible for an interested student to learn the difficult subject of electromagnetic field theory by presenting many worked examples emphasizing physical processes devices and models. The problems at the back of each chapter are grouped by chapter sections and extend the text material. To avoid tedium most integrals needed for problem solution are supplied as hints. The hints also often suggest the approach needed to obtain a solution easily. Answers to selected problems are listed at the back of this book. A NOTE TO THE INSTRUCTOR An Instructor s Manual with solutions to all exercise problems at the end of chapters is available from the author for the cost of reproduction and mailing. Please address requests on University or Company letterhead to Prof. Markus Zahn Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Cambridge MA 01239 CONTENTS Chapter 1 REVIEW OF VECTOR ANALYSIS 1 COORDINATE SYSTEMS 2 Rectangular Cartesian Coordinates 2 Circular Cylindrical Coordinates 4 Spherical Coordinates 4 VECTOR ALGEBRA 7 Scalars and Vectors 7 Multiplication of a Vector by a Scalar 8 Addition and Subtraction 9 The Dot Scalar Product 11 The Cross Vector Product 13 THE GRADIENT AND THE DEL OPERATOR 16 The Gradient 16 Curvilinear Coordinates 17 a Cylindrical 17 b Spherical 17 The Line Integral 18 FLUX AND DIVERGENCE 21 Flux 22 Divergence 23 Curvilinear Coordinates 24 a Cylindrical Coordinates 24 b Spherical Coordinates 26 The Divergence Theorem 26 THE CURL AND STOKES THEOREM 28 Curl 28 The Curl for Curvilinear Coordinates 31 a Cylindrical Coordinates 31 b Spherical Coordinates 33 Stokes Theorem 35 Some Useful Vector Relations 38 a The Curl of the Gradient is Zero Vx V 0 38 b The Divergence of .
