Electromagnetic Fields and Waves

Other Books this Book deals with theory, the rest of it is application of this theory to various situations of different levels of complexity. In each case the reason for the choice of the method is explained, and various doubts which assail the minds of most students have been tackled. The solved examples in the book do not deal with mere substitution of numerical Values of formulae. They are aimed at establishing a strong foundation of knowledge.

All the required Mathematics has been explained in the first chapter to avoid the need to refer frequently to other Books in mathematics. At the end of each chapter a summary of the achievements is given along with comments on the Nature of difficulties encountered, and the reader is thereafter prepared for the objectives to be attained in the following chapter. The emphasis throughout the book is on a Physical understanding of Fields and waves and their characteristics, rather than getting lost in a maze of Mathematical manipulations. This is an introductory textbook intended to give the reader a Solid grounding in the subject and to prepare him to deal with more Advanced texts. The Material has been tested in one-semester courses given by the author in various colleges in Pune.

Maharashtra Institute of Technologyon-Institute-of-India" Title="Film-and-Television-Institute-of-India">Film and Television Institute of Indiahref="../books/University" Title="University">University for a post-graduate degree in Communication Engineering in 1946. From 1948 to 1964 he served in Government Engineering College, Jabalpur, M.P. where he was Professor and Head of Department of Telecommunication Engineering.

In 1964, Prof. Sarwate was promoted as a Principal and posted a Bilaspur, M.P. and later at Raipur. Then he became the Director of Technical Education, Madhya Pradesh at Bhopal. After retirement in 1977 he settled in Pune where he continued his hobby of Teaching by giving Lectures on Electromagnetic Fields and Waves to Final Year B.E. students in College of Engineering, Maharashtra Institute of Technology and Bharati
Vidyapeeths College of Engineering. He also teaches in the Film and Television Institute of India as a Guest Lecturer.

Preface

Chap. I : NEEDED Mathematics :
1. Binomial Theorem
2. Exponential Series
3. Logarithms
4. Exponential Theorem and Logarithmic Series
5. Number System Using Ordered Pairs
6. Complex Numbers
7. Natural and Hyperbolic Sines and Cosines
8. Co-ordinate Systems
9. Differential Calculus, Integral Calculus and Differential Equations
10. Fourier Series
11. Vector Analysis
12. Vector Algebra
13. Vector Differential Operator
14. Unit Vectors &; Differential Elements of Volume
15. Del Operator in the Three Co-ordinate Systems
16. Standard Curves

Chap. II : COULOMB'S Law AND STATIC ELECTRIC Fields :
1. Coulomb's Law
2. Permittivity
3. Comments on Coulomb's Law
4. Electric Field Intensity
5. Electrical Field Map with Direction Lines
6. Equation to Direction Line on Field Map
7. Electric Field Map for a Point Charge
8. Electric Field Map-of Two Like and Equal Point Charges
9. Electric Field Map of Two Unlike and Equal Charges (Electric Dipole)
10. Electric Field Map of Uniformly Charged Short Line
11. Uniformly Charged Infinite Line
12. Field Map of Two Infinite Parallel Lines with Equal and Opposite Uniform Linear Charges
13. Uniformly Charged Circular Loop
14. Uniformly Charged Circular Disk
15. Electric Field of Uniformly Charged Infinite Plane
16. Electric Field of Two Uniformly but Oppositely Charged Parallel Infinite Planes
17. Electric Field of Uniformly Charged Spherical Surface
18. Electric Field of Spherical Shell with Uniform Volume Charge Density
19. Summary of Results and Comments

Chap. III : POTENTIAL AND ITS GRADIENT :
1. Line Integral of a Vector
2. Conservative and Non-conservative Vector Fields
3. Electric Potential, Potential Energy and Potential Difference
4. Equipotential Lines on Potential Maps
5. Potential Gradient
6. Map with Equipotential and Direction Lines
7. Equipotential for a Point Charge +Q
8. Equipotentials for an Electric Dipole
9. Equipotentials for Uniformly Charged Short Line
10. Equipotentials for Uniformly Charged Infinite Line
11. Equipotential Map for Infinite Parallel Lines with Equal and Opposite Uniform Linear Charges
12. Summary and Comments

Chap. IV : GAUSS'S LAW :
1. Faraday's Experiment
2. Electrical Displacement or Flux
3. Mie Plates
4. Lines and Tubes of Electric Displacement or Flux
5. Gauss's Law
6. Procedure for Applying Gauss's Law
7. Electric Field of Infinite Plane with Uniform Charge Density
8. Electric Field of Uniformly Charged Infinite Line
9. Electric Field of Uniformly Charged Spherical Shell
10. Electric Field of a Cylindrical Electron Beam
11. Electric Field of a Uniform Volume Charge Distribution in Cartesian Co-ordinates
12. Conductors, Conductivity and Current Density
13. Corollaries about Conductors Deduced from Gauss's Law
14. Capacitance
15. Parallel Plate Capacitor
16. Concentric Spheres Forming a Capacitor
17. Capacitance Per Metre Length of a Co-axial Cable
18. Capacitance Per Metre Length of Two-wire Line
19. Divergence and Divergence Theorem
20. Applying Gauss's Law in Differential Vector Form
21. Summary and Comments

Chap V : METHOD OF Images AND CONFORMAL Transformations :
1. Geometrical Optics
2. Image of Point Charge in Infinite Conducting Plane
3. Multiple Images
4. Image of Uniformly Charged Infinite Line in Infinite Plane
5. Image of Point Charge in Grounded Conducting Circular Ring
6. Image of a Uniform Line Charge in a Parallel Conducting Cylinder
7. Image of Point Charge in Conducting Sphere
8. Infinite Conducting Plane Placed in Field of a Point Charge
9. Capacitance of a Capacitor Formed by a Conducting Sphere Near a Conducting Infinite Plane
10. Effect of Placing Conducting Cylinder Across Uniform Electric Field
11. Conformal Transformations
12. Orthogonal Properties of Conjugate Functions
13. Exponential Transformation w = ez
14. Logarithmic Transformation w = logez
15. Power Function Transformation w = azn
16. Summary and Comments

Chap. VI : POISSON'S EQUATION AND LAPLACE'S EQUATION :
1. Poisson's Equation
2. Child's Law for Space-charge Limited Current in a High Vacuum Diode
3. Laplace's Equation
4. Product Solution of Laplace Equation by Separation of Variables in Cartesian Co-ordinates
5. Rectangular Harmonic Solution
6. Series Solution Using Rectangular Harmonics
7. Cylindrical Harmonics
8. Conducting Cylinder in Uniform Field
9. Spherical Harmonic Solution for Conducting Sphere in Uniform Field
10. Graphical Solution of Laplace's Equation
11. Summary and Comments

Chap. VII : CONDUCTORS AND DIELECTRICS :
1. Conductors
2. Effect of Placing a Conductor in Electric Field
3. Dielectrics
4. Electric Polarization
5. Effect of Placing a Dielectric in Electric Field
6. Field Maps for Dielectric Cylinder and Sphere Placed in Uniform Electric Field
7. Table of Dielectric Constants
8. Boundary Conditions in Electric Fields
9. Summary and Comments

Chap. VIII : MAGNETOSTATICS :
1. Magnetic Field Produced by Electric Current
2. Magnetic Flux
3. Magnetic Flux Density or Magnetic Induction
4. Magnetic Field Intensity
5. Biot-savart Law or Ampere's Current Law
6. Force on Current Element in Magnetic Field
7. Force between Current Elements
8. Line Integral of Magnetic Field Intensity
9. Magnetic Flux Through Completely Enclosed Surface
10. Magnetic Field Intensity Due to a Short, Straight Current Element
11. Magnetic Field Intensity Due to Current in a Conductor of Finite Diameter
12. Magnetic Field Intensity Due to Infinite Plane Sheet of Current
13. Toroidal Coil
14. Infinitely Long Solenoid
15. Vector Magnetic Potential
16. Vector Magnetic Potential of a Current Element Ids
17. Magnetic Field Intensity Around Infinitely Long, Straight Conductor
18. Infinite Parallel Line
19. Magnetic Dipole
20. Self-inductance and Mutual Inductance
21. Boundary Conditions in Magnetic Fields
22. Summary and Comments

Chap. IX : MOVING CHARGES IN ELECTRIC AND MAGNETIC FIELD :
1. Introduction
2. Moving Charge in Electric Field
3. Moving Electric Charge in Uniform Magnetic Field
4. Lorentz Equation
5. Electrostatic Deflection in a Cathode Ray Tube
6. Magnetostatic Deflection in a Cathode Ray Tube
7. Parallel Plate Magnetron
8. Mass Spectrograph
9. Summary and Comments

Chap. X : MAXWELL'S EQUATIONS :
1. Ampere's Circuital (Work) Law in Differential Vector Form
2. Stoke's Theorem
3. Comments on Eq. (10.2)
4. Equation of Continuity
5. Maxwell's First Equation
6. Displacement Current
7. Maxwell's Second Equation
8. Maxwell's Third and Fourth Equations
9. Summary and Comments

Chap. XI : TIME-VARYING FIELDS AND ELECTROMAGNETIC WAVES :
1. Solution of Maxwell's Equations for Charge-free Unbounded Region
2. Uniform Waves
3. Uniform Plane Waves
4. Relation between E and H in a Uniform Plane Wave
5. Polarization
6. Wave Equations for a Charge-free Medium with Finite Conductivity
7. Characteristic Wave Impedence and Propagation Constant
8. Classification of Medium as Dielectric or Conductor
9. Wave Propagation in a Good Dielectric
10. Wave Propagation in a Good Conductor
11. Depth of Penetration in a Good Conductor
12. Surface Impedance of Good Conductor to Sinusoidal Currents
13. Summary and Comments

Chap. XII : WAVES AT BOUNDARY BETWEEN TWO MEDIA :
1. Introduction
2. Wave Incident Normally on Boundary between Perfect Dielectrics
3. Wave Incident Obliquely on Boundary between Perfect Dielectrics
4. Wave Polarized Perpendicular to the Plane of Incidence
5. Wave Polarized Parallel to Plane of Incidence
6. Wave Incident Normally on Perfect Conductor
7. Use of Direction Cosines
8. Plane Wave Incident Obliquely on Perfect Conductor with Electric Vector Perpendicular to Plane of Incidence
9. Plane Wave Incident Obliquely on Perfect Conductor with Electric Vector Parallel to Plane of Incidence
10. Summary and Comments

Chap. XIII : THE POYNTING VECTOR :
1. Energy Storage in Electric Field
2. Energy Storage in Magnetic Field
3. Poynting Vector for a Plane Wave in a Dielectric
4. Poynting's Theorem
5. Flow of Direct Current in Cylindrical Resistor
6. Flow of Direct Current in Co-axial Cable
7. Poynting Vector with Time-varying Fields
8. Summary and Comments

Chap. XIV : GUIDED WAVES AND WAVE GUIDES :
1. Essential Conditions for Guided Waves
2. TEM Waves in Co-axial Cables and Two-wire Transmission Lines
3. TE Waves Guided between Parallel Conducting Planes
4. Rectangular Wave Guide
5. Electric and Magnetic Fields Inside Rectangular Waveguide
6. Solution of Wave Equations for Rectangular Waveguide
7. Transverse Electric Wave in Rectangular Waveguide
8. Transverse Magnetic Wave in Rectangular Waveguide
9. Cut-off Frequency and Wavelength
10. Dominant TE10 Mode
11. Lowest Frequency Transverse Magnetic Tm11 Mode
12. Circular Waveguides
13. Cavity Resonators
14. Phase Velocity and Group Velocity
15. Summary and Comments

Chap. XV : ANTENNA AND ANTENNA ARRAYS :
1. Retarded Magnetic Vector Potential
2. Magnetic and Electric Fields of Oscillating Hertzian Dipole
3. Radiation Field of Hertzian Dipole Antenna
4. Poynting Vector and Radiation Resistance of Short Dipole Antenna
5. Quarter-wave Monopole and Half-wave Dipole
6. Antenna Gain and Effective Length of a Half-wave Dipole
7. Directional Characteristics of Antenna
8. Radiation Pattern of Dipole Antenna
9. Folded Dipole and Yagi Antenna
10. Antenna Arrays
11. Array of Two-element Isotropic Radiators
12. Linear Array of Isotropic Radiators
13. Multiplication of Patterns
14. Four and Eight Element Arrays
15. Binomial Arrays
16. Effect of Earth on Vertical Pattern
17. Three-dimensional Rectangular Array of Identical Radiators
18. Summary and Comments

Chap. XVI : PROPAGATION CHARACTERISTICS OF Radio WAVES :
1. The Electromagnetic Wave Spectrum
2. Transmission Paths from Transmitter to Receiver
3. The Ionosphere
4. Ionospheric Investigation
5. Virtual Height and Critical Frequency
6. Maximum Usable Frequency
7. Effect of Earth's Magnetic Field
8. Skip Distance
9. Ionospheric Behaviour Variations
10. Sky Wave Propagation
11. Great Circle Distances on Earth
12. Ground Wave Propagation
13. Space Wave Propagation
14. Space Wave Propagation Affected by Atmosphere
15. Problems of Space Wave Propagation
16. Propagation Characteristics of Radio Waves, 3 to 100 kHz
17. Propagation Characteristics of Radio Waves, 100 to 535 kHz
18. Propagation Characteristics of Radio Waves, 535 to 1605 kHz
19. Propagation Characteristics of Short Waves, 1.605 to 30 MHz
20. Propagation Characteristics of VHF, UHF and Microwaves
21. Tropospheric Scatter Propagation
22. Noise, Atmospherics and Man-made Static
23. Summary and Comments