Analysis and Computation of Electric and Magnetic Field Problems

Analysis and Computation of Electric and Magnetic Field Problems

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

2nd Edition - January 1, 1973

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  • Authors: K. J. Binns, P. J. Lawrenson
  • eBook ISBN: 9781483151625

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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.

Table of Contents

  • 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


    Part II: Direct Methods

    Chapter 3 Images

    3.1 Introduction

    3.2 Plane Boundaries

    3.3 Circular Boundaries

    3.4 General Considerations


    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


    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


    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


    Chapter 7 Curved Boundaries

    7.1 The Bilinear Transformation

    7.2 The Simple Joukowski Transformation

    7.3 Curves Expressible Parametrically: General Series Transformations


    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


    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


    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


    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


    Chapter 12 The Monte Carlo Method

    12.1 Introduction

    12.2 The Method

    12.3 Example

    12.4 Some General Points



    Appendix I The Sums of Certain Fourier Series

    Appendix II Series Expansions of Elliptic Functions

    Appendix III Table of Transformations

    Appendix IV Bibliographies


Product details

  • No. of pages: 336
  • Language: English
  • Copyright: © Pergamon 1973
  • Published: January 1, 1973
  • Imprint: Pergamon
  • eBook ISBN: 9781483151625

About the Authors

K. J. Binns

P. J. Lawrenson

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