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About the BookAbout the AuthorTable of Contents

This is an introductory textbook on electromagnetic fields suitable for undergraduate engineering courses in electrical engineering. It adopts a straightforward approach of presenting theoretical concepts in brief and using several worked-out examples of varied kinds to provide a further understanding of concepts. The material covered in the book broadly aims to develop formulations associated with the analysis of electrostatic, static magnetic and time-varying electromagnetic fields. A review of vector calculus, included as an appendix, provides the necessary mathematical background for understanding the treatment.
The salient features of the book are:

clear and concise explanations
a number of worked-out examples
variety in exercises
a coverage that matches the undergraduate curriculum
inclusion of several problems drawn from previous university question papers

Y Mallikarjuna Reddy, Principal, Vasireddy Venkitadri Institute of Technology, Nambur, Guntur, is a professor in the department of Electronics and Communications Engineering. He has more than 22 years of teaching experience. He obtained his MTech degree from JNTU Kakinada in 1990 and his PhD in 2009 from Osmania University, Hyderabad. He is a member of I(E) and ISTE, India. He has published research papers in journals of international repute and is currently engaged in research in the areas of radar signal and image processing.

Preface
Electrostatics

Introduction to Electrostatic Fields
Coulomb’s Law
Force in Terms of Rectangular Coordinates
Force Due to N Number of Charges
Electric Field Intensity (E)
Charge Distributions
Electric Field Intensity Due to Charge Distributions
Electric Field Due to Infinite Line Charge
Electric Field Due to Finite Line Charge
Electric Field Strength Due to a Circular Ring of Charge
Electric Field Strength Due to an Infinite Sheet of Charge
Electric Field Strength Due to a Sheet of Circular Disc
Electric Field Strength at the Centre of a Half Circular Ring
Electric Flux and Flux Density
Electric Flux Density Due to Point Charge Q
Electric Flux Density Due to Charge Distributions
Gauss’ Law (Integral Form)
Gauss’ Law in Point Form (Maxwell’s First Law)
Divergence of Electric Flux Density
Divergence Theorem of Electric Flux Density
Electric Flux Density Due to Infinite Line Charge Using Gauss’ Law
Flux Density Due to an Infinite Sheet Charge Using Gauss’ Law
Flux Density for a Coaxial Cable
Flux Density for a Spherical Shell of Charge
Flux Density for a Uniformly Charged Sphere
Work Done in Moving a Point Charge in an Electrostatic Field
Electric Potential
Potential Due to Point Charge
Potential Due to N Point Charges
Potential Due to Charge Distribution
Potential Difference Due to an Infinite Line Charge
Potential Due to a Line Charge of Finite Length Potential Due to a Circular Ring
Potential Gradient
Relationship between E and V: Maxwell’s Second Equation
Potential Function (V)
Equipotential Surfaces
Additional Problems
Questions
Problems
Answers Multiple-Choice Questions
Answers

Conductors and Dipole

Introduction
Conductors
Behaviour of Conductors in an Electric Field
Electric Dipole
Potential Due to Electric Dipole
Dipole Moment
Electric Field Due to Dipole
Torque on an Electric Dipole in an Electric Field
Torque on a Dipole Due to the Field of Another Dipole
Poisson’s and Laplace’s Equations
Uniqueness Theorem
Electric Field between Two Concentric Conducting Spheres Using Laplace’s Equation
Electric Field of a Coaxial Cable Using Laplace’s Equation
Electric Field Due to Semi Infinite Conducting Planes
Electric Field Due to Two Axial Conducting Cones
Additional Problems
Questions
Problems
Answers
Multiple-Choice Questions
Answers

Dielectrics and Capacitance

Dielectric Materials
Polarization
Electric Displacement Vector in Dielectrics
Boundary Conditions
Capacitance
Capacitance between Two Concentric Spheres
Capacitance of a Coaxial Cable
Capacitance of Two Parallel Wires (Single-Phase Transmission Line)
Energy Stored in an Electrostatic Field
Energy Stored in Terms of E and D
Energy Stored in a Capacitor
Energy Stored in a Coaxial Cable
Electric Current and Current Density
Current Density
Conductors and Conductivity
Point Form of Ohm’s Law (Relationship between J and E
Relationship between J and rv
Continuity Equation
Relaxation time (Tr )
Resistance and Power
Additional Problems
Questions
Problems
Answers
Multiple-Choice Questions
Answers

Magnetostatics

Introduction
Density
Additional Problems
Questions
Problems
Answers

Multiple-Choice Questions
Answers

Ampere’s Circuital Law and Its Applications

Introduction
Ampere’s Circuital Law or Ampere’s Work Law
Magnetic Field Intensity Due to a Solid Conductor
Magnetic Field Intensity Due to Coaxial Cable
Magnetic Field Intensity Due to an Infinite Sheet of Current
Magnetic Field Intensity at Any Point in between Two
Infinite Parallel Surface Current Sheets
Differential or Point Form of Ampere’s Circuital Law (Maxwell’s Third Equation)
Stokes’ Theorem
Point Form of Magnetic Flux Density
Magnetic Field Intensity Due to a Solenoid Using Ampere’s Circuital Law
Magnetic Field Intensity Due to a Toroid Using Ampere’s Circuital Law
Additional Problems
Questions
Problems
Answers
Multiple-Choice Questions
Answers

Force in Magnetic Fields

Introduction
Force and Torque on a Moving Charge
Force on a Differential Current Element
Ampere’s Force Law: Force Between Two Current Elements
Force between Two Straight Infinitely Long Parallel Conductors
Magnetic Torque Due to Rectangular Loop in a Magnetic Field
Magnetic Dipole and Dipole Moment
Boundary Conditions for Magnetic Field
Additional Problems
Questions
Problems
Answers
Multiple-Choice Questions
Answers

Magnetic Potential and Inductance

Introduction
Scalar Magnetic Potential ( Vm )
Magnetic Potential at the Centre of a Square Loop
Vector Magnetic Potential ( A)
The Vector Magnetic Potential for Line Current Element
Poisson’s Equation for Vector Magnetic Potential
Properties of Vector Magnetic Potential
Vector Magnetic Potential in the Field Due to Infinite Length Conductor
Vector Magnetic Potential Due to a Straight Line of Finite Length
Inductor and Inductance
Inductance of a Solenoid
Inductance of a Toroid
Inductance of a Coaxial Cable
Inductance of a Two-Wire Transmission Line
Mutual Inductance
Neumann’s Formula for Mutual Inductance
Mutual Inductance between Two Solenoids
Magnetic Energy
Energy Density Stored in the Magnetic Field
Energy Stored Due to Mutual Inductance
Magnetic Circuits
Magnetic Materials
Characteristics of Magnetic Materials
Additional Problems
Questions
Problems
Answers
Multiple-Choice Questions
Answers

Time-Varying Fields

Introduction
Faraday’s Law
Induced EMF in an AC Generator
Induced EMF in a Coil
Faraday’s Disc Generator
Equation of Continuity for Time-Varying Fields
Modified Ampere’s Circuital Law for Time-Varying Fields
Displacement Current
Ratio between Conduction Current Density and Displacement Current Density
Differences between Conduction, Convection and Displacement Currents
Differences between Displacement Current Density and Conduction Current Density
Maxwell’s Equations for Static Fields
Maxwell’s Equation for Sinusoidal (Harmonic) Time-Varying Fields
Boundary Conditions
Poynting Theorem
Additional Problems
Questions
Problems
Answers
Multiple-Choice Questions
Answers

Appendix A: Review of Vector Algebra

Definitions
Distance Vector
Vector Addition
Vector Multiplication
Dot Product
Cross Product
Scalar Triple Product
Vector Triple Product
The Cartesian or Rectangular Coordinate System
Circular Cylindrical Coordinate System
Spherical Coordinate System
Differential Elements
Transformation of Vectors
Gradient, Divergence and Curl of a Vector
Vector Identities
Del Operators

Appendix B: Symbols of Quantities
Index