Designed according to the syllabus of the undergraduate electrical engineering programme in India, this book adopts a straightforward approach of presenting theoretical concepts and several worked-out examples in their support. The discussions begin with a review of vector calculus, the essential mathematical tool for analysis in electromagnetic theory. Elements of electrostatics, magnetostatics, time-varying electric and magnetic fields, wave propagation through unbounded and bounded mediums and the transmission lines theory are covered concisely to give readers a sound introduction to the subject and its engineering applications.

* Salient features

* Clear and concise explanations of fundamental concepts

* Includes a chapter on guided waves

* Emphasis on problem solving and review of core concepts with the help of

* 350 Solved examples

* Over 200 practice problems and an equal number of review questions

* Nearly 400 multiple-choice questions

Y Mallikarjuna Reddy, Principal, Vasireddy Venkatadri Institute of Technology, Nambur, Guntur, is a professor in the department of Electronics and Communication Engineering. He has more than 23 years of teaching experience, which includes research, guiding PhD students and administration at various levels. He obtained his BE (1987) from Osmania University, MTech (1990) from JNTU Kakinada and PhD (2009) from Osmania University for his work on radar signal processing. His areas of interest are DSP, radar, speech processing and missile technology. He has published his research work in reputed journals and is the author of Probability Theory and Stochastic Processes, and Electromagnetic Fields, both textbooks for undergraduate engineering programmes. He is a life member of the Institution of Engineers, India, and ISTE, India.

TABLE OF CONTENTS

Preface 

1. Introduction to Vector Fields

1.1 Introduction 

1.2 Basic Definitions 

1.3 Vector Addition and Subtraction 

1.4 Vector Multiplication 

1.4.1 Dot Product 

1.4.2 Cross Product 

1.5 Triple Products 

1.5.1 Scalar Triple Product 

1.5.2 Vector Triple Product 

1.6 Orthogonal Coordinate System 

1.6.1 Cartesian or Rectangular Coordinate System 

1.6.2 Circular Cylindrical Coordinate System 

1.6.3 Spherical Coordinate System 

1.7 Transformation of Vectors 

1.8 Differential Elements 

1.9 Line, Surface and Volume Integrals 

1.10 Gradient, Divergence and Curl of a Vector 

1.11 Del Operators 

1.12 Useful Theorems 

Summary 

Review Questions 

Problems 

Multiple choice Questions 

2. Electrostatics

2.1 Introduction to Electrostatic Fields 

2.2 Coulomb’s law 

2.3 Force in Terms of Rectangular Coordinates 

2.4 Force due to N Number of Charges 

2.5 Electric Field Intensity (E) 

2.6 Charge Distributions 

2.7 Electric Field Intensity due to Charge Distributions 

2.8 Electric Field due to Infinite Line Charge 

2.9 Electric Field due to a Finite Line Charge 

2.10 Electric Field Strength due to a Circular Ring of Charge 

2.11 Electric Field Strength due to an Infinite Sheet of Charge 

2.12 Electric Field Strength due to a Sheet of Circular Disc 

2.13 Electric Flux and Flux Density 

2.14 Electric Flux Density due to Point Charge Q 

2.15 Electric Flux Density due to Charge Distributions 

2.16 Gauss’ Law (Integral Form) 

2.17 Gauss’ Law in Point Form (Maxwell’s First Law) 

2.18 Divergence of Electric Flux Density 

2.19 Divergence Theorem of Electric Flux Density 

2.20 Electric Flux Density due to an Infinite Line Charge Using Gauss’ Law 

2.21 Flux Density due to an Infinite Sheet Charge Using Gauss’ Law 

2.22 Flux Density for a Coaxial Cable 

2.23 Flux Density for a Spherical Shell of Charge 

2.24 Flux Density for a Uniformly Charged Sphere 

2.25 Work Done in Moving a Point Charge in an Electrostatic Field 

2.26 Electric Potential 

2.27 Potential due to a Point Charge 

2.28 Potential due to Point Charges 

2.29 Potential due to Charge Distribution 

2.30 Potential Difference due to an Infinite Line Charge 

2.31 Potential due to a Line Charge of Finite Length 

2.32 Potential due to a Circular Ring 

2.33 Potential Gradient 

2.34 Relationship between E and V: Maxwell’s Second Equation 

2.35 Potential Function (V ) 

2.36 Equipotential Surfaces 

2.37 Electric Dipole 

2.38 Potential due to an Electric Dipole 

2.39 Dipole Moment 

2.40 Electric Field due to a Dipole 

2.41 Torque on an Electric Dipole in an Electric Field 

2.42 Energy Stored in an Electrostatic Field 

2.43 Energy Stored in Terms of E and D 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions vii

3. Electric Fields in Conductors and Dielectrics

3.1 Introduction 

3.2 Conductors 

3.3 Behaviour of Conductors in an Electric Field 

3.4 Electric Current (I) 

3.5 Current Density (J) 

3.6 Ohm’s Law and Conductivity 

3.7 Relationship between J and rv 

3.8 Point Form of Ohm’s Law (Relationship between J and E) 

3.9 Dielectric Materials 

3.10 Polarization 

3.11 Electric Displacement Vector in Dielectrics 

3.12 Continuity Equation 

3.13 Relaxation Time (Tr) 

3.14 Resistance and Power 

3.15 Boundary Conditions 

3.16 Poisson’s and Laplace’s Equations 

3.17 Uniqueness Theorem 

3.18 Electric Field between Two Concentric Conducting Spheres Using 

Laplace’s Equation 

3.19 Electric Field due to Coaxial Cable Using Laplace’s Equation 

3.20 Electric Field due to Semi Infinite Conducting Planes 

3.21 Electric Field due to Two Axial Conducting Cones 

3.22 Capacitance 

3.23 Capacitance between Two Concentric Spheres 

3.24 Capacitance of a Coaxial Cable 

3.25 Capacitance of Two Parallel Wires (Single-Phase Transmission Line) 

3.26 Energy Stored in a Capacitor 

3.27 Energy Stored in a Coaxial Cable 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions 

4. Magnetostatics

4.1 Introduction 

4.2 Magnetic Field due to a Current-Carrying Conductor 

4.3 Magnetic Flux and Flux Density 

4.4 Biot–Savart’s Law 

4.5 Biot–Savart’s Law for Distributed Currents 

4.6 Oersted’s Experiment 

4.7 Magnetic Field Intensity due to an Infinitely Long Conductor 

4.8 Magnetic Field Intensity due to a Finite Length Conductor 

4.9 Magnetic Field Intensity along the Axis of a Circular Loop 

4.10 Magnetic Field Intensity at the Centre of an Equilateral Triangle Formed by a Wire of Length L 

4.11 Magnetic Field Intensity (H) at the Centre of a Square Formed by a Current-Carrying Wire of Length L 

4.12 Magnetic Field Intensity due to a Regular Polygon 

4.13 Magnetic Field Intensity due to a Solenoid 

4.14 Maxwell’s Equation for Magnetic Flux Density 

4.15 Ampere’s Circuital Law or Ampere’s Work Law 

4.16 Magnetic Field Intensity due to a Solid Conductor 

4.17 Magnetic Field Intensity due to a Coaxial Cable 

4.18 Magnetic Field Intensity due to an Infinite Sheet of Current 

4.19 Magnetic Field Intensity at Any Point in between Two Infinite Parallel Surface Current Sheets 

4.20 Differential or Point Form of Ampere’s Circuital Law (Maxwell’s Third Equation) 

4.21 Stokes’ Theorem 

4.23 Point Form of Magnetic Flux Density 

4.24 Magnetic Field Intensity due to a Solenoid using Ampere’s Circuital Law 

4.25 Magnetic Field Intensity due to a Toroid using Ampere’s Circuital Law 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions 

5. Magnetic Force and Inductance 

5.1 Introduction 

5.2 Scalar Magnetic Potential (Vm) 

5.3 Magnetic Potential at the Centre of a Square Loop 

5.4 Vector Magnetic Potential (A) 

5.5 Vector Magnetic Potential in the Field due to an Infinite Length Conductor 

5.6 Vector Magnetic Potential in the Field due to Finite Length Conductor 

5.7 Force and Torque on a Moving Charge 

5.8 Force on a Differential Current Element 

5.9 Ampere’s Force Law: Force Between Two Current Elements 

5.10 Force between Two Straight, Infinitely Long Parallel Current Carrying Conductors 

5.11 Magnetic Torque due to a Rectangular Differential Current Loop in a Magnetic Field 

5.12 Magnetic Dipole and Dipole Moment 

5.13 Boundary Conditions for Magnetic Field 

5.14 Inductor and Inductance 

5.15 Mutual Inductance 

5.16 Neumann’s Formula for Mutual Inductance 

5.17 Mutual Inductance between Two Solenoids 

5.18 Magnetic Energy 

5.19 Energy Density Stored in the Magnetic Field 

5.20 Energy Stored due to Mutual Inductance 

5.21 Magnetic Circuits 

5.22 Magnetic Materials 

5.23 Characteristics of Magnetic Materials 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions 

6. Time-Varying Fields 

6.1 Introduction 

6.2 Faraday’s Law 

6.3 Induced EMF in an AC Generator 

6.4 Induced EMF in a Coil 

6.5 Equation of Continuity for Time-Varying Fields 

6.6 Modified Ampere’s Circuital Law for Time-Varying Fields 

6.7 Displacement Current 

6.8 Ratio between Conduction Current Density and Displacement Current Density 

6.9 Conduction, Convection and Displacement Currents 

6.10 Maxwell’s Equations for Static Fields 

6.11 Maxwell’s Equation for Sinusoidal (Harmonic) Time-Varying Fields 

6.12 Boundary Conditions 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions

7. Electromagnetic Waves 

7.1 Introduction 

7.2 Wave Equations in a Homogeneous Medium 

7.2.1 Wave Equations for a Perfect Dielectric (Free Space) 

7.2.2 Wave Equations for a Conducting Medium 

7.3 Time Harmonic Wave Equations (Phasor Notation) 

7.4 Uniform Plan Wave Propagation 

7.5 Solution for the Uniform Plane Wave Equation 

7.6 Characteristic Impedance 

7.7 Wave Propagation in a Conducting Medium 

7.8 Characteristic Impedance in a Lossy Dielectric or Conducting Medium 

7.9 Wave Propagation in Perfect Dielectric Medium 

7.10 Expressions for a and b for a Conducting Medium 

7.11 Wave Propagation in Good Conductors 

7.12 Wave Propagation in Good Dielectrics 

7.13 Depth of Penetration (Skin Depth d ) 

7.14 Polarization of a Uniform Plane Wave 

7.14.1 Linear Polarization 

7.14.2 Circular Polarization 

7.14.3 Elliptical Polarization 

7.15 Direction Cosines of a Vector Field 

Additional Solved Problems 

Summary 

Review Questions 

Exercise Problems 

Multiple-choice Questions 

8. Electromagnetic Wave Characteristics

8.1 Introduction 

8.2 Reflection and Refraction of a Uniform Plane Wave 

8.3 Reflection by a Perfect Conductor with Normal Incidence 

8.4 Reflection by a Perfect Dielectric—Normal Incidence 

8.5 Reflection of a Plane Wave—Oblique Incidence 

8.6 Reflection of a Horizontally Polarized Wave by a Perfect Conductor—Oblique Incidence 

8.7 Reflection of a Vertically Polarized Wave by a Perfect Conductor—Oblique Incidence 

8.8 Reflection by a Dielectric or Perfect Insulator—Oblique Incidence 

8.9 Brewster Angle 

8.10 Total Internal Reflection 

8.11 Surface Impedance 

8.12 Surface Resistance and Surface Reactance 

8.13 Poynting Vector and Poynting Theorem 

8.14 Poynting Theorem 

8.15 Power Loss in a Plane Conductor 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions 

9. Transmission Lines - I

9.1 Introduction 

9.2 Types of Transmission Lines 

9.2.1 Transmission Line Parameters 

9.3 Transmission Line Equations 

9.4 Infinite Length Line

9.5 Transmission Line Terminated with Characteristic Impedance Z0 

9.6 Derivation of Attenuation and Phase Shift Constants 

9.7 Velocity of Propagation and Group Velocity 

9.8 Relationship between Group Velocity and Phase Velocity 

9.9 Lossless Transmission Line 

9.10 Distortionless Transmission Line 

9.11 High Frequency Transmission Line 

9.12 Telephone Cable 

9.13 Condition for Minimum Attenuation 

9.14 Line Distortion 

9.15 Conditions to Achieve Minimum Attenuation 

9.16 Loaded Line 

Additional Solved Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions

10. Transmission Lines - II 

10.1 Introduction 

10.2 Standing Waves on a Transmission Line 

10.3 Open and Short-Circuited Lines 

10.4 Input Impedance of Open and Short-Circuited Lines 

10.5 Transmission Line with Load Impedance 

10.6 Voltage and Current Distributions on a Lossless Line 

10.7 Reflection and Reflection Coefficients 

10.8 Standing Wave Ratio 

10.9 Input Impedance in Terms of Reflection Coefficient 

10.10 Location of Voltage Maxima and Minima 

10.11 Impedance Transformation 

10.12 Input Impedance of Lossless SC and OC Transmission Lines 

10.13 UHF Lines as Circuit Elements 

10.14 Stub Matching 

10.15 Single Stub Matching 

10.16 Double Stub Matching 

10.17 Smith Chart 

10.18 Properties of the Smith Chart 

10.19 Applications of the Smith Chart 

10.20 Single Stub Matching Using Smith Chart 

10.21 Double Stub Matching Using Smith Chart 

Additional Solved Problems

Problems Using Smith Chart

Summary 

Review Questions 

Problems 

Multiple-choice Questions 

11. Guided Waves 

11.1 Introduction 

11.2 Waves between Parallel Planes 

11.3 Transverse Electric Waves 

11.4 Transverse Magnetic Waves 

11.5 Characteristics of TE and TM Waves 

11.6 Velocities of Wave Propagation 

11.7 Transverse Electromagnetic Waves (TEM Waves) 

11.8 Attenuation of Guided Waves 

11.9 Wave Impedances 

11.10 Relationship between Wave Impedance and Cutoff Frequency 

11.11 Fields and Current Flow within the Conductor 

11.12 Attenuation of Wave Modes 

Additional Problems 

Summary 

Review Questions 

Problems 

Multiple-choice Questions 

Appendix-A 

Appendix-B 

Index