# Foundations of Electrical Engineering

### Fields—Networks—Waves

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Foundations of Electrical Engineering covers the fundamental ideas and basic laws in electrical engineering. This book is organized into five parts encompassing 24 chapters. Part I provides an overview of the Maxwell's equation and its significance in electrical engineering. Part II deals first with the determination of static and steady electric fields. This part also discusses the solution of Laplace's equation, boundary value problems, the concept of capacity, and magnetic field. Parts III and IV explore the laws of network analysis and synthesis, as well as the basic principles and applications of electromagnetic waves. These parts also describe the main features of classical electrodynamics and its application to problems of electrical engineering. Part V highlights the combined contributions of Maxwell's equations and the laws of mechanics in the subject field. Electrical engineers, and electrical engineering teachers and students will find this book invaluable.

## Table of Contents

Foreword

Part I General Survey

1. Introduction

2. The Inductive Approach to Maxwell's Equations

(a) The Biot Savart Law

(b) The Concept of Displacement Current and Maxwell's First Law

(c) Maxwell's Second Equation

3. The Complete Set of Maxwell's Equations

4. Simplified Forms of Maxwell's Equations

(a) Maxwell's First Equation

(b) Maxwell's Second Equation

(c) Order of Magnitude of the Displacement Current

(d) The Remaining Equations

(e) Maxwell's Equations for Alternating Fields

5. Maxwell's Equations in More General Form

(a) More General Formula for Material Constants e and µ

(b) The Physical Significance of the Individual Terms in Maxwell's Equations

(c) Moving Media

6. The Behavior of the Electromagnetic Field at Surfaces Separating Materials with Differing Characteristics

7. Energy Conversion in the Electromagnetic Field

(a) General Relations

(b) Poynting's Vector

(c) Energy Flow in Constant Fields

(d) Further Special Examples of Energy Conversion

(e) Forces in the Electromagnetic Field

8. The Uniqueness of the Solution of Maxwell's Equations

9. Local Action — Action at a Distance

10. Systems of Units

11. The Measurement of Basic Electromagnetic Units

12. The Subdivisions of Electrodynamic Theory

13. Summary of the Basic Concepts of Vector Algebra and Vector Analysis

(a) The Basic Concepts of Vector Algebra

(b) The Derivative of a Function in Three Dimensional Space

(c) The Concept of the Divergence and Curl of a Vector

(d) Multiple Vector Operations

(e) A Useful Alternative Notation

(f) Integral Theorems

(g) Green's Theorem for Vector Functions

14. The Inverse of Certain Vector Operations

(a) The Determination of a Scalar Given Its Gradient

(b) The Determination of a Vector Given Its Divergence or Curl

(c) The Irrotational Field Containing Sources

(d) The Source Free Rotational Field

(e) The Irrotational Source Free Field of Finite Extent

(f) The Determination of a Vector Field of Finite Extent Given Its Sources and Curl

Part II Static and Steady Fields

A. The Determination of the Electric Field from a Given Charge Distribution

1. The Determination of The Field from a Given Space Charge Density

2. Dipoles and Multipoles

3. The Calculation of the Electric Field Due to Surface Charges and Dipole Sheets

4. The Geometric Significance of the Potential of a Double Layer

5. The Physical Explanation of the Sudden Change in Potential and Field Strength

6. The Replacement of Space Charge by a Closed Surface Carrying Surface Charge and a Double Layer

7. The Practical Significance of the Results Obtained above

B. The Determination of Simple Three Dimensional Fields from Given Boundary Conditions

8. Problems of Practical Electrostatics

9. The Basic Concepts of Vector Analysis and Maxwell's Equations Expressed in Orthogonal Curvilinear Coordinates

10. The Solution of Laplace's Equation — Some Simple Three Dimensional Problems

C. The Solution of Plane Boundary Value Problems

11. Solution by Separation of the Variables

12. Solution in Power Series

13. The Elementary Properties of Functions of a Complex Variable. Conformal Transformation

14. The Solution of a Two Dimensional Problem by Means of Complex Functions

15. Examples of the Use of Functions of a Complex Variable

16. A Fundamental Theorem of Conformal Transformation Theory

17. The Field Due to Electrodes of Polygonal Cross-Section

18. Examples of the Use of the Schwarz-Christoffel Transformation

D. Cylindrically Symmetrical Fields

19. The Determination of the Electrostatic Field Due to Cylindrically Symmetrical Electrodes by the Method of Separation of the Variables

20. The Solution of Bessel's Equation. The Properties of Bessel Functions

21. Examples of the Determination of Cylindrically Symmetrical Fields of Force

22. The Calculation of the Potential When The Potential Distribution on the Axis is Known

23. The Solution of the Cylindrically Symmetrical Form of Laplace's Equation by Series Development

24. The General Solution of Laplace's Equation in Cylindrical Coordinates

E. The Solution of Laplace's Equation in Spherical Coordinates

25. The Treatment of Cylindrically Symmetrical Fields by Means of Spherical Functions

26. The Properties of Legendre Polynomials

27. The General Solution of Laplace's Equation in Spherical Coordinates

28. The Properties of Associated Legendre Functions

29. The Development of the Function 1/r in Terms of Spherical Functions

30. Development in Series in Terms of Spherical Functions

31. The Use of Spherical Functions in Solving Electrostatic Problems

F. Special Methods of Solving Potential Problems

32. The Method of Images

33. Numerical Methods Applicable to Plane Problems

34. The Electrolytic Tank

35. The Monte Carlo Method

36. The Graphical Evaluation of Plane and Cylindrically Symmetrical Fields

37. The Theory of the Rubber Model

G. Boundary Value Problems in Potential Theory

38. Green's Function in Three Dimensional Space

39. Green's Function in Two Dimensional Space

40. Solution by Means of Integral Equations

H. The Generalization of the Concept of Capacity

41. The Concept of Capacity Coefficients

42. The Energy of the Electrostatic Field

I. The Static Field in the Presence of Matter

43. The Electrostatic Field in Insulators

44. The Magnetostatic Field

45. Examples of the Calculation of Electrostatic and Magnetostatic Fields in the Presence of Matter

J. The Magnetic Field Due to Steady Currents

46. The Calculation of the Magnetic Field by Means of Vector Potential

47. The Derivation of the Magnetic Field from a Cyclic Potential

48. Examples of the Determination of the Vector Potential

49. The Calculation of Cylindrically Symmetrical Magnetic Fields

50. The Concept of Coefficients of Inductance

51. The Energy in the Magnetic Field

52. Methods of Calculation of Self and Mutual Inductance

53. Elliptic Integrals and Elliptic Functions

54. Singularities in the Magnetic Field

55. The Magnetic Field Due to Steady Currents in the Presence of Ferromagnetic Materials

Part III Network Analysis and Network Synthesis

A. The Laws of Network Analysis

1. Kirchhoff's Equations

2. The Most General Formulation of Kirchhoff's Equations 339

3. Networks with Sinusoidal Time Variation

4. Frequency Dependence of the Immittance Functions of General Networks

5. Nonlinear Networks

B. The Laws of Network Synthesis

6. Analysis for the Purpose of Synthesis

7. Basic Problems in Network Synthesis

8. Realization of Reactive Networks

9. Realization of General Two-Terminal Networks

C. Transient Phenomena

10. The Classical Method

11. The Method of the Step Function or Impulse Function

12. Calculation of Transients When the Frequency Spectrum of the Voltage is Known

13. The Laplace Transformation

14. The Application of the Laplace Transformation to Simple Circuits

15. The Elementary Method of Inverting the Laplace Transformation

16. Examples of the Application of the Laplace Transformation

17. Further Theorems in the Theory of Complex Functions

18. The Inversion of the Laplace Transformation

D. Quasi Steady State Spatial Currents

19. The Concepts of Resistance and Induction-Coefficient for Spatial Currents

20. Electromagnetic Field in Materials with Finite Conductivity

21. The Electromagnetic Field in Semi-Infinite Conducting Medium

22. The Resistance of a Semi-Infinite Conducting Medium

23. The Electromagnetic Field in a Laminated Semi-Infinite Medium

24. The Resistance of a Laminated Semi-Infinite Medium

25. The Electromagnetic Field in Circular Cylindrical Conductors

26. The Impedance of Cylindrical Conductors

27. Laminated Cylindrical Conductors

28. The Resistance of Laminated Cylindrical Conductors

29. Induction Heating

30. Skin Effect in the Slots of Electrical Machines

31. Eddy Currents in Thin Plates

E. Transmission Lines

32. Derivation of the Transmission Line Equations

33. Solution of the Transmission Line Equations

34. Propagation Coefficient and Characteristic Impedance as Functions of the Line Parameters

35. Phenomena at the End of the Line

36. The Input Impedance of the Transmission Line

37. The Finite Line as Circuit Element

38. Transmission Lines with Non-Uniform Characteristic Impedance

39. Transients on Ideal Transmission Lines

40. Application of the Laplace Transformation to the Investigation of Transients on Transmission Lines

41. Transients on Lines of Finite Length

42. Examples of the Calculation of Transients on Finite Transmission Lines

43. The General Problem of Infinite Cables

Part IV Electromagnetic Waves

A. Plane Waves

1. The Simplest Solution of the Wave Equation

2. The Reflexion of Plane Waves at Conductors and Insulators

3. Plane Waves in Matter Possessing Finite Conductivity

4. Plane Waves in Gyromagnetic Media

B. Linear Antennas and Antenna Arrays

5. The Solution of Maxwell's Equations by Means of Retarded Potentials

6. The Solution of Maxwell's Equations for a Dielectric by Means of the Hertz Vector

7. The Radiation from a Dipole

8. The Radiation from a Loop Antenna

9. Radiation from Linear Antennas with Arbitrarily Chosen Current Distribution

10. The Influence of the Earth on the Radiation Field

11. The Radiation Impedance of a Linear Antenna

12. The Reciprocity Theorem

C. The Solution of the Wave Equation in Different Coordinate Systems

13. The Reduction of the Vector Wave Equation to the Scalar Wave Equation

14. Homogeneous and Inhomogeneous Plane Waves

15. Cylindrical Waves

16. Spherical Waves

17. Mutual Relations between Plane, Cylindrical and Spherical Waves

D. Boundary Value Problems

18. The Refraction and Reflexion of Plane Waves

19. The Propagation of Waves along a Circular Cylinder

20. The Solution of the Boundary Value Problem on a Spherical Surface

21. The Calculation of the Radiation Field of a Dipole Antenna Situated on Ground of Finite Conductivity

E. Boundary Value Problems. II Waves in Waveguides

22. Qualitative Treatment of Waves in Waveguides

23. The Calculation of the Field Strength within a Waveguide of Arbitrary Cross-Section

24. The Circular-Cylindrical Waveguide

25. Solutions Satisfying the Boundary Conditions

26. The Limiting Wavelength

27. The Properties of Some Simple Modes

28. Modes in Coaxial Cables

29. Modes in Elliptical Waveguides

30. Waves in Rectangular Waveguides

31. Comparison of Circular Waveguides, Rectangular Waveguides, and Coaxial Cables

32. The Characteristic Impedance of a Waveguide

33. The Calculation of the Power Propagated in a Waveguide

34. Losses in Waveguides

35. The Excitation of Waves in Waveguides

36. Waveguides Containing Ferrite

F. Boundary Value Problems. III Cavity Resonators

37. The Cylinder as Cavity Resonator

38. The Sphere as Cavity Resonator

39. Figure of Merit and Circuit Parameters of a Cavity Resonator

G. General Radiation Problems

40. Huyghen's Principle: Scalar Form

41. Huyghen's Principle: Vectorial Form

42. Babinet's Principle in the Electromagnetic Field

Part V Survey of Further Developments

1. Magnetohydrodynamics

2. Relativistic Formulation of Maxwell's Equations

(a) The Lorentz Transformation

(b) Maxwell's Equations and the Lorentz Transformation

(c) The Lorentz Invariant Formulation of Maxwell's Equations

(d) Some Results of Relativistic Electrodynamics

3. The Fundamental Principles of Quantum Electrodynamics

(a) The Basic Purpose

(b) Recapitulation of the Fundamental Equations of a Mechanical System Possessing a Large But Finite Number of Degrees of Freedom

(c) Analogy Between Mechanical and Electrical Systems

(d) The Fundamental Classical Equations for Continuous Media

(e) Maxwell's Equations Expressed in Mechanical Terms

(f) The Principles of Quantum Mechanics

(g) The Fundamental Relations of Quantum Electrodynamics

(h) Some Consequences of Quantum Electrodynamics

List of References

Notation for the Most Important Quantities

Name and Subject Index

## Product details

- No. of pages: 864
- Language: English
- Copyright: © Pergamon 1963
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483222288

## About the Author

### K. Simonyi

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