Foundations of Electrical Engineering

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.

ForewordPart 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 CurlPart 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 MaterialsPart 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 CablesPart 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 FieldPart 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 ElectrodynamicsList of ReferencesNotation for the Most Important QuantitiesName and Subject Index

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