Analysis and Computation of Electric and Magnetic Field Problems

Description

Analysis and Computation of Electric and Magnetic Field Problems, Second Edition is a comprehensive treatment of both analytical and numerical methods for the derivation of two-dimensional static and quasi-static electric and magnetic fields. The essence of each method of solution is emphasized and the scopes of the different methods are described, with particular regard to the influence of digital computers.
This book is comprised of 12 chapters and begins with an introduction to the fundamental theory of electric and magnetic fields. The derivation of quantities of physical interest such as force, inductance, and capacitance from the field solution is explained. The next section deals with the methods of images and separation of variables and presents direct solutions of Laplace's equation and of Poisson's equation. The basic solutions are developed rigorously from considerations of surface charges and are expressed in complex variable form. Subsequent chapters discuss transformation methods as well as line and doublet sources; the transformation of regions exterior to finite boundaries; and the powerful numerical methods used to enlarge the scope of conformal transformation. The last section is devoted to finite difference methods and the Monte Carlo method, along with all classes of boundary shape and condition.
This monograph is intended primarily for engineers, physicists, and mathematicians, as well as degree students towards the end of their courses.

Front Cover 2
Analysis and Computation of Electric and Magnetic Field Problems 5
Copyright Page 6
Table of Contents 7
Preface 13
PART I: INTRODUCTION 15
- CHAPTER 1. INTRODUCTION 17
- CHAPTER 2. BASIC FIELD THEORY 21
  - 2.1. Electric fields 21
  - 2.2. Magnetic fields 30
  - 2.3. Boundary conditions 37
  - 2.4. Conjugate functions 39
  - 2.5. Equivalent pole and charge distributions 44
  - 2.6. Forces 46
  - References 47

Front Cover 2
Analysis and Computation of Electric and Magnetic Field Problems 5
Copyright Page 6
Table of Contents 7
Preface 13
PART I: INTRODUCTION 15
- CHAPTER 1. INTRODUCTION 17
- CHAPTER 2. BASIC FIELD THEORY 21
  - 2.1. Electric fields 21
  - 2.2. Magnetic fields 30
  - 2.3. Boundary conditions 37
  - 2.4. Conjugate functions 39
  - 2.5. Equivalent pole and charge distributions 44
  - 2.6. Forces 46
  - References 47
- PART II: DIRECT METHODS 49
  - CHAPTER 3. IMAGES 51
    - 3.1. Introduction 51
    - 3.2. Plane boundaries 52
    - 3.3. Circular Boundaries 60
    - 3.4. General considerations 68
    - References 71
    - Additional Reference 71
  - CHAPTER 4. THE SOLUTION OF LAPLACE'S EQUATION BY SEPARATION OF THE VARIABLES 73
    - 4.1. Introduction 73
    - 4.2. Circular boundaries 74
    - 4.3. Rectangular boundaries 86
    - 4.4. Conclusions 94
    - References 95
    - Additional References 96
  - CHAPTER 5. THE SOLUTION OF POISSON'S EQUATION: MAGNETIC FIELDS OF DISTRIBUTED CURRENT 97
    - 5.1. Introduction 97
    - 5.2. Non-magnetic conductors in air 99
    - 5.3. The field inside infinitely permeable conductors in air 105
    - 5.4. Simple boundaries: use of the image method 108
    - 5.5. The treatment of boundaries using single Fourier series: Rogowski's method 109
    - 5.6. The treatment of boundaries using double Fourier series: Roth's method 117
    - References 126
    - Additional References 127
  - PART III: TRANSFORMATION METHODS 129
    - CHAPTER 6. INTRODUCTION TO CONFORMAL TRANSFORMATION 131
      - 6.1. Conformal transformation and conjugate functions 131
      - 6.2. Classes of solvable problems 137
      - 6.3. General considerations 138
      - 6.4. The determination of transformation equations 142
      - References 142
    - CHAPTER 7. CURVED BOUNDARIES 143
      - 7.1. The bilinear transformation 143
      - 7.2. The simple Joukowski transformation 154
      - 7.3. Curves expressible parametrically: general series transformations 159
      - References 163
      - Additional References 163
    - CHAPTER 8. POLYGONAL BOUNDARIES 165
      - 8.1 Introduction 165
      - 8.2. Transformation of the upper half plane into the interior of a polygon 166
      - 8.3. Transformation of the upper half plane into the region exterior to a polygon 191
      - 8.4 Transformations from a circular to a polygonal boundary 196
      - 8.5. Classification of integrals 200
      - References 201
      - Additional References 202
    - CHAPTER 9. THE USE OF ELLIPTIC FUNCTIONS 203
      - 9.1. Introduction 203
      - 9.2. Elliptic integrals and functions 204
      - 9.3. The field outside a charged rectangular conductor 210
      - 9.4. The field in a slot of finite depth 222
      - 9.5. Conclusions 227
      - References 228
      - Additional References 228
    - CHAPTER 10. GENERAL CONSIDERATIONS 231
      - 10.1. Introduction 231
      - 10.2. Field sources 231
      - 10.3. Curved boundaries 238
      - 10.4. Angles not multiples of π/2 241
      - 10.5. Numerical methods 242
      - 10.6. Non-equipotential boundaries 249
      - References 251
      - Additional References 252
    - PART IV: NUMERICAL METHODS 253
      - CHAPTER 11. FINITE-DIFFERENCE METHODS 255
        
        11.1. Introduction 255
        
        11.2. Finite-difference representation 256
        
        11.3. Hand computation: relaxation 262
        
        11.4. Machine computation: iteration 272
        
        11.5. Gradient boundary conditions 282
        
        11.6. Errors 293
        
        References 299
        
        Additional References 300
      - CHAPTER 12. THE MONTE CARLO METHOD 303
        
        12.1. Introduction 303
        
        12.2. The method 303
        
        12.3. Example 305
        
        References 306
        
        Additional References 306
        
        12.4. Some general points 306
      - APPENDIX I: THE SUMS OF CERTAIN FOURIER SERIES 307
      - APPENDI X II: SERIES EXPANSIONS OF ELLIPTIC FUNCTIONS 309
      - APPENDIX III: TABLE OF TRANSFORMATIONS 313
      - APPENDIX IV: BIBLIOGRAPHIES 329
      - INDEX 333

Pergamon International Library of Science, Technology, Engineering and Social Studies

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