2D Electrostatic Fields

A Complex Variable Approach

Robert L. Coffie (RLC Solutions, USA.)

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English

CRC Press
09 October 2024

Mathematical physics; Maths for engineers; Electronics engineering; Microwave technology

This book demonstrates how to use functions of a complex variable to solve engineering problems that obey the 2D Laplace equation (and in some cases the 2D Poisson equation). The book was written with the engineer/physicist in mind and the majority of the book focuses on electrostatics. A key benefit of the complex variable approach to electrostatics is the visualization of field lines through the use of field maps. With todays’ powerful computers and mathematical software programs, field maps are easily generated once the complex potential has been determined. Additionally, problems that would have been considered out of scope previously are now easily solved with these mathematical software programs. For example, solutions requiring the use of non-elementary functions such as elliptic and hypergeometric functions would have been viewed as not practical in the past due to the tedious use of look up tables for evaluation. Now, elliptic and hypergeometric functions are built-in functions for most mathematical software programs making their evaluation as easy as a trigonometric function. Key highlights in the book include

2D electrostatics completely formulated in terms of complex variables

More than 60 electrostatic field maps

Comprehensive treatment for obtaining Green’s functions with conformal mapping

Fully worked Schwarz-Christoffel transformations to more than usual number of problems

A full chapter devoted to solving practical problems at an advanced level

Detailed solutions to all end of chapter problems available on book’s website

Although the text is primarily self-contained, the reader is assumed to have taken differential and integral calculus and introductory courses in complex variables and electromagnetics.

By: Robert L. Coffie (RLC Solutions USA.)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9780367769765
ISBN 10: 036776976X
Pages: 362
Publication Date: 09 October 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Forthcoming

1. Functions of a Complex Variable. 2. Electrostatics. 3. Line Charges. 4. Conformal Mapping I. 5. Conformal Mapping II. 6. Case Studies with Conformal Mapping. 7. Other Fields of Physics. Appendix A. Differentiating an Integral. Appendix B. Dirac δ-Function. Appendix C. Elliptic Integrals. Appendix D. Jacobi’s Elliptic Functions. Appendix E. Gamma and Beta Functions. Appendix F. Gauss’s Hypergeometric Function. Appendix G. Dilogarithm and Trilogarithm Functions.

Robert L. Coffie is the Founder and President of RLC Solutions, a semiconductor/microelectronics consulting company. He has designed, developed and matured AlGaN/GaN high electron mobility transistor (HEMT) technologies for RF applications from L-band to Q-band at Northrop Grumman and TriQuint Semiconductor (now Qorvo). He also developed the first JEDEC qualified AlGaN/GaN HEMTs for 600 V power switching applications at Transphorm where he served as Director of Device Engineering.