Analysis and Computation of Electric and Magnetic Field Problems

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

2nd Edition - January 1, 1973
Authors: K. J. Binns, P. J. Lawrenson
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 5 1 6 2 - 5

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… Read more

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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.

Preface

Part I: Introduction

Chapter 1 Introduction

Chapter 2 Basic Field Theory

2.1 Electric Fields

2.2 Magnetic Fields

2.3 Boundary Conditions

2.4 Conjugate Functions

2.5 Equivalent Pole and Charge Distributions

2.6 Forces

References

Part II: Direct Methods

Chapter 3 Images

3.1 Introduction

3.2 Plane Boundaries

3.3 Circular Boundaries

3.4 General Considerations

References

Chapter 4 The Solution of Laplace's Equation by Separation of the Variables

4.1 Introduction

4.2 Circular Boundaries

4.3 Rectangular Boundaries

4.4 Conclusions

References

Chapter 5 The Solution of Poisson's Equation: Magnetic Fields of Distributed Current

5.1 Introduction

5.2 Non-magnetic Conductors in Air

5.3 The Field inside Infinitely Permeable Conductors in Air

5.4 Simple Boundaries: Use of the Image Method

5.5 The Treatment of Boundaries using Single Fourier Series: Rogowski's Method

5.6 The Treatment of Boundaries using Double Fourier Series: Roth's Method

References

Part III: Transformation Methods

Chapter 6 Introduction to Conformal Transformation

6.1 Conformal Transformation and Conjugate Functions

6.2 Classes of Solvable Problems

6.3 General Considerations

6.4 The Determination of Transformation Equations

References

Chapter 7 Curved Boundaries

7.1 The Bilinear Transformation

7.2 The Simple Joukowski Transformation

7.3 Curves Expressible Parametrically: General Series Transformations

References

Chapter 8 Polygonal Boundaries

8.1 Introduction

8.2 Transformation of the Upper Half Plane into the Interior of a Polygon

8.3 Transformation of the Upper Half Plane into the Region Exterior to a Polygon

8.4 Transformations from a Circular to a Polygonal Boundary

8.5 Classification of Integrals

References

Chapter 9 The Use of Elliptic Functions

9.1 Introduction

9.2 Elliptic Integrals and Functions

9.3 The Field outside a Charged Rectangular Conductor

9.4 The Field in a Slot of Finite Depth

9.5 Conclusions

References

Chapter 10 General Considerations

10.1 Introduction

10.2 Field Sources

10.3 Curved Boundaries

10.4 Angles Not Multiples of π/2

10.5 Numerical Methods

10.6 Non-Equipotential Boundaries

References

Part IV: Numerical Methods

Chapter 11 Finite-Difference Methods

11.1 Introduction

11.2 Finite-difference Representation

11.3 Hand Computation: Relaxation

11.4 Machine Computation: Iteration

11.5 Gradient Boundary Conditions

11.6 Errors

11.7 Conclusions

References

Chapter 12 The Monte Carlo Method

12.1 Introduction

12.2 The Method

12.3 Example

12.4 Some General Points

References

Appendixes

Appendix I The Sums of Certain Fourier Series

Appendix II Series Expansions of Elliptic Functions

Appendix III Table of Transformations

Appendix IV Bibliographies

Index