Foundations of Electrical Engineering
Fields—Networks—Waves
- 1st Edition - January 1, 1963
- Imprint: Pergamon
- Author: K. Simonyi
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 5 1 0 4 - 5
Foundations of Electrical Engineering: Fields—Networks—Waves describes the general principles of electrical engineering, with emphasis on fields, networks, and waves. The… Read more
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Request a sales quoteFoundations of Electrical Engineering: Fields—Networks—Waves describes the general principles of electrical engineering, with emphasis on fields, networks, and waves. The limitations of validity are defined and methods of calculation are outlined. Examples are used to illustrate the theory and microphysical explanations based on simple models are given. This book is divided into five sections and begins with an overview of the inductive approach to Maxwell's equations, along with the uniqueness of their solution. Energy conversion in the electromagnetic field as well as the basic concepts of vector algebra and vector analysis are also considered. Subsequent chapters focus on static and steady fields, including cylindrically symmetrical fields and magnetic fields; the laws of network analysis and network synthesis; transient phenomena; and transmission lines. The remaining sections deal with electromagnetic waves, with emphasis on boundary value problems, and further developments in electrical engineering. This monograph will be of interest to students of electrical engineering and mathematics.
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 ε 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) Pointing'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
(6) 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
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. I
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
- Edition: 1
- Published: January 1, 1963
- No. of pages (eBook): 865
- Imprint: Pergamon
- Language: English
- eBook ISBN: 9781483151045
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