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Analysis and Computation of Electric and Magnetic Field Problems
Pergamon International Library of Science, Technology, Engineering and Social Studies
- 2nd Edition - October 22, 2013
- Authors: K. J. Binns, P. J. Lawrenson
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 1 9 2 0 - 5
- 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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Request a sales quoteAnalysis 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
- No. of pages: 336
- Language: English
- Edition: 2
- Published: October 22, 2013
- Imprint: Pergamon
- Paperback ISBN: 9781483119205
- eBook ISBN: 9781483151625
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