Foreword Preface
Acknowledgements
Timeline of Progress in Electromagnetic Theory and Related Areas
1 Introduction
1.1 What is the Objective of the Book?
1.2 Why is the Title of the Book So Chosen?
1.3 What Mathematical Background is Required?
1.4 What Are You Going to Get in This Book?
2 Vector Calculus Expressions for Gradient, Divergence and Curl
Why curvilinear coordinate system?
2.1 Representation of a Point in Different Coordinate Systems
2.2 Volume Elements in Different Coordinate Systems
2.3 Element of Distance Vector Directed from One Point to Another
2.4 Line Integral and Surface Integral or Flux of a Vector Quantity
2.5 Gradient of a Scalar Quantity
2.6 Divergence of a Vector Quantity
2.7 Curl of a Vector Quantity
2.8 Laplacian of Scalar and Vector Quantities
Appendix A2.1: Relation of cylindrical and spherical coordinates with rectangular coordinates
Appendix A2.2: Description of the volume element
Sumarising Notes
Review Questions
3 Basic Concepts of Static Electric Fields
3.1 Coulomb’s Law and Gauss’s Law of Electrostatics
3.1.1 Coulomb’s law of electrostatics
3.1.2 Electric field and electric displacement due to a point charge
3.1.3 Gauss’s law of electrostatics
Illustrative Examples of Applications of Gauss’s Law
(a) Electric field due to a point charge from Gauss’s law
(b) Electric field due to a long line charge from Gauss’s law
(c) Electric field due to a large sheet of charge from Gauss’s law
(d) Electric field due to a charged plane conductor from Gauss’s law
(e) Electric field inside a long beam of electrons from Gauss’s law
3.1.3.A Gauss’s law from Coulomb’s law
3.1.3.B Gauss’s law in terms of a volume charge density
3.1.3.C Gauss’s law for predicting Coulomb’s law
3.2 Electric Field and Potential
3.2.1 Electric potential due to a point charge
3.2.2 Electric field in terms of potential gradient
3.3 Poisson’s and Laplace’s Equations
3.3.1 Laplacian form of Poisson’s and Laplace’s Equations
(a) Electric field in a region between the plates of a parallel-plate capacitor
(b) Child-Langmuir’s law for a planar space-charge limited diode
Appendix A3.1: Electric displacement
Sumarising Notes
Review Questions
4 Basic Concepts of Static Magnetic Fields
4.1 Laws of Magnetostatics
4.1.1 Coulomb’s law of magnetostatics, magnetic field and flux and
flux density due to a magnetic charge
4.1.2 Gauss’s law and Poisson’s equation of magnetostatics
4.2 Biot-Savart’s Law
4.3 Ampere’s Circuital Law
4.3.1 Ampere’s circuital law in integral form
4.3.2 Ampere’s circuital law in differential form
4.4 Lorentz Force on a Moving Charge and Force on a Current-carrying Conductor in a Magnetic Field
4.4.1 Lorentz force
4.4.2 Force on a current-carrying conductor
4.5 Magnetic Vector Potential due to a Steady Current
Appendix A4.1: Magnetic field due to a direct current passing through a straight wire of a finite length
Appendix A4.2: Deduction of the relation:
Appendix A4.3: Behaviours of some non-conventional media: Anisotropic, ferrite/gyromagnetic and bi-isotropic/chiral
Sumarising Notes
Review Questions
5 Basic Concepts of Time-varying Electric and Magnetic Fields
5.1 Continuity Equation and Relaxation Time in Physical Media
5.1.1 Continuity equation
5.1.2 Relaxation time in physical media
5.2 Time-Varying Magnetic Field and Faraday’s Law
5.2.1 Integral form of Faraday’s law
5.2.2 Differential form of Faraday’s law
5.3 Time-varying Electric Field and Displacement Current
5.4 Maxwell’s Equations
5.5 Electric Scalar Potential and Magnetic Vector Potentials in Time-varying Fields
5.5.1 Retarded scalar and vector potentials
Appendix A5.1: Electric field inside the conducting sheet and the dielectric sheets placed in an electric field
Appendix A5.2: Expression for the current in a circuit that is linked up with a magnetic flux density varying with time
Appendix A5.3: Phasor representation of a time periodic quantity
Appendix A5.4: Phasor diagram depicting current density and electric field in an imperfect dielectric to find the loss tangent of the dielectric
Sumarising Notes
Review Questions
6 Wave Equation and Its Solution for a Wave Propagating through an Unbounded Medium
6.1 Representation of a Quantity Associated with a Wave
6.2 Wave Propagation through a Free-Space Medium
6.3 Wave Propagation through a Conducting Medium
6.4 ac or RF Resistance
6.5 Wave Propagation through Seawater
6.6 Wave Propagation through a Medium of Charged Particles
Appendix A6.1: Polarisation of a wave
Summarising Notes
Review Questions
7 Electromagnetic Boundary Conditions
7.1 General Boundary Conditions
7.2 Boundary Conditions at Dielectric-Dielectric Interface
7.3 Boundary Conditions at Conductor-Dielectric Interface
7.4 Boundary Conditions at Conductor-Conductor Interface for Time-independent Situations: Refraction of Currents
7.5 Reflection of Electromagnetic Waves at the Interface between a Dielectric/Free-Space and a Conductor
7.6 Reflection and Refraction of Electromagnetic Waves at a Dielectric-Dielectric Interface 7.6.1 Reflection and transmission coefficients for parallel polarisation
7.6.2 Reflection and transmission coefficients for perpendicular polarisation
7.6.3 Total internal reflection
7.7 Boundary Conditions for a Structure Model
Appendix A7.1: An alternative approach to deriving expression (7.100) for magnetic field from that for the electric field
Summarising Notes
Review Questions
8 Electromagnetic Power Flow
8.1 Energy Stored in Electrostatic and Magnetostatic Fields
8.2 Poynting Theorem for Energy Balance in Electromagnetic Power Flow
8.2.1 Poynting theorem involving instantaneous Poynting vector
8.2.2 Complex Poynting vector theorem and time-averaged electromagnetic power flow
8.2.3 Poynting theorem in the presence of an external source
8.2.4 Poynting theorem in different versions revisited
8.3 Power Loss in Electromagnetic Wave Propagation at a Conducting Boundary
8.4 Radiated and Received Powers in Conduction Current Antennas
8.4.1 Infinitesimal dipole antenna
8.4.2 Constancy of the ratio of effective aperture area to directive gain of an antenna
8.4.3 Finite-length dipole antenna
8.5 Array of Antennas
8.5.1 Broadside array
8.5.2 End-fire array
Appendix A8.1: Separation of ? = (j?µ0/s)1/2 into its real and imaginary parts
Appendix A8.2: Finding ??. for given by (8.145)
Appendix A8.3: Far-field and near-field zones of an antenna
Appendix A8.4: Generalised expressions for the radiation resistance and directive gain of a finite-length dipole
Summarising Notes
Review Questions
9 Waveguides: Solution of the Wave Equation for a Wave in a Bounded Medium
9.1 Rectangular Waveguide in Transverse Electric Mode
9.1.1 Wave equation
9.1.2 Field solutions
9.1.3 Characteristic equation or dispersion relation
9.1.4 Characteristic parameters
9.1.5 Evanescent mode
9.1.6 Dimension-wise and mode-wise operating frequency criteria
9.2 Rectangular Waveguide in Transverse Magnetic Mode
9.3 Significance of Mode Numbers vis-à-vis Field Pattern
9.4 Cylindrical Waveguide
9.5 Power Flow and Power Loss in a Waveguide
9.5.1 Power flow
9.5.2 Power loss per unit area and power loss per unit length
9.5.3 Attenuation constant from power flow and power loss per unit length
Appendix A9.1: Wave group velocity
Appendix A9.2: Bessel functions
Appendix A9.3: Relation between Neper and decibel
Summarising Notes
Review Questions
10 Waveguide Resonator: Analytic Appreciation by Equivalent Transmission Line Approach
10.1 Basics of Transmission Line Theory
10.1.1 Telegrapher’s equations of a transmission line
10.1.2 Circuit potential and current on a transmission line terminated in a load impedance
10.1.3 Distortionless transmission line
10.1.4 Reflection coefficient of the line
10.1.5 Input impedance of the line
10.1.6 Characteristic impedance of the line
10.1.7 Voltage standing-wave ratio (VSWR) of the line
10.1.7.A Prediction of the load impedance from the standing-wave patterns
10.1.8 Smith chart
10.1.8.A Reflection coefficient and the constant-|Gl| circle
10.1.8.B Constant-r and constant-x circles
10.1.8.C Location of load impedance on the chart
10.1.8.D Reading of VSWR
10.1.8.E Location of input impedance
10.1.8.F Location of admittance
10.1.8.G Impedance maximum and minimum in the standing-wave
10.1.8.H Load impedance from the standing-wave patterns
10.1.8.I Attenuation constant of a lossy transmission line
10.1.9 Impedance transformer
10.1.9.A Quarter-wave transformer
10.1.9.B Single-stub and double-stub impedance transformer
10.2 Resonant Length and Resonant Frequency of a Waveguide Resonator
10.3 Fields in a Waveguide Resonator
10.4 Energy Stored and Power Dissipated in a Waveguide Resonator
10.4.1 Energy stored
10.4.2 Power dissipation
10.5 Quality Factor of a Resonator
Appendix A10.1 Impedance maxima and minima on a transmission line
Appendix A10.2 Load impedance from the shift in the standing-wave pattern due to a short replacing the load
Appendix A10.3 Algebraic steps leading to the derivation of equations for generating constant-r and constant-x circles of the Smith chart
Summarising Notes
Review Questions
11 Summary
Constants, Properties and Relations
Vector Calculus Expressions
Bibliography
Index