Engineering Electromagnetics Essentials
B N Basu
120 x 180 mm
Year of Publishing
Territorial Rights
Universities Press
This book deals with the fundamentals of electromagnetics of relevance to engineering. It begins with a concise and clear introduction to vector calculus, essential for the development of em theory concepts from first principles. The topics in the book are chosen with care to ensure that readers are able to grasp the essence of engineering electromagnetics within a reasonable time; the approach adopted attempts to make the learning both enjoyable and meaningful. Interesting illustrative examples and thought-provoking chapter-end problems are included to inspire students to take up more challenging problems of practical relevance.

Help is available in the book in the form of complete solutions/hints, with due references to the concepts developed in the book.

Salient features

  • Covers all the elementary concepts required to appreciate the engineering applications of the subject
  • Derivations and explanation of all essential mathematical treatments elaborated to make the learning enjoyable
  • Carefully chosen illustrative problems that lead to new learnings
  • Challenging exercises that invite readers to develop interesting concepts of relevance to engineering disciplines

Further help for teachers is available at

B. N. Basu, who superannuated as Professor and Head, Electronics Engineering Department, Banaras Hindu University (BHU), Varanasi, is presently Professor Emeritus at the Sir J. C. Bose School of Engineering, Mankundu, West Bengal. Professor Basu, who was Distinguished Visiting Scientist at Central Electronics Engineering Research Institute (CEERI), Pilani, is presently Visiting Professor at CEERI under the Academy of Scientific and Innovative Research of CSIR. He is Consultant at Microwave Tube Research and Development Centre (MTRDC), Bengaluru (DRDO), and is associated with a number of national laboratories (CSIR and DRDO) as an advisor and reviewer of projects. He is a member of the DST Steering Committee of the multi-institutional project, Gyrotron, as well as the Research Council of DRDO, Ministry of Defence at MTRDC.

He has authored or co-authored more than 115 research papers in journals of international repute and six monograph chapters in the area of microwave tubes. He has also authored two books: Electromagnetic Theory and Applications in Beam-Wave Electronics (World Scientific, Singapore/New Jersey/London/Hong Kong, 1996) and Technical Writing (Prentice-Hall of India, New Delhi, 2007).
Foreword Preface 


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 


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