Electromagnetics Made Easy

Preface
Contents
About the Author
1 Vector Analysis
	1.1 Introduction
	1.2 Graphical Representation of Vectors
	1.3 Symbolic Representation of Vectors
	1.4 Vector Addition
	1.5 Subtraction of Vectors
	1.6 Multiplication of a Vector by a Scalar
	1.7 Multiplication of Vectors: Dot Product of Two Vectors
	1.8 Multiplication of Vectors—Cross—Product of Two Vectors
	1.9 Vector Components and Unit Vectors
	1.10 Triple Products
	1.11 Line, Surface and Volume Integration
	1.12 Flux
	1.13 Vector Differentiation: Gradient of a Scalar Function
	1.14 Vector Differentiation: Divergence of a Vector
	1.15 Vector Differentiation: Curl of a Vector
	1.16 Divergence Theorem
	1.17 Stoke’s Theorem
	1.18 The Gradient Theorem
	1.19 Others Coordinate Systems
		1.19.1 Spherical Polar Coordinates
		1.19.2 Cylindrical Coordinates
	1.20 Important Vector Identities
	1.21 Two and Three Dimensions
	Exercises
2 Electric Charges at Rest: Part I
	2.1 Coulomb’s Law
	2.2 Electric Field Intensity
	2.3 Electric Field Intensity Due to a Group of Discrete Point Charges
	2.4 Continuous Charge Distributions
	2.5 A Note about Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.6 Calculating Electric Field E Using Coulomb’s Law
	2.7 Solid Angle
	2.8 Gauss’s Law
	2.9 Sketches of Field Lines
	2.10 Curl of E
	2.11 Potential of Discrete and Continuous Charge Distributions
	2.12 Calculating Electric Field Using Gauss’s Law and Potential
	2.13 Electric Field Due to an Infinite Line Charge
	2.14 Electric Field Due to the Finite Line Charge
	2.15 Electric Field Along the Axis of a Uniformly Charged Circular Disc
	2.15 Electric Field Along the Axis of a Uniformly Charged Circular Disc
	2.16 Electric Field Due to an Infinite Plane Sheet of Charge
	2.17 Electric Field of a Uniformly Charged Spherical Shell
	2.18 Comparison of Coulomb’s Law, Gauss’s Law and Potential Formulation
	2.19 Electric Field of a Dipole
	2.20 Calculation of Potential Using {\\rm V} = \\int\\limits {{{\\bf E}}\\cdot{\\hbox{d}}{\\varvec l}}
	2.21 The Conservative Nature of Electric Field
	2.22 The Reference Point R in the Equation {\\hbox{V}} = - \\int\\limits_{{\\rm R}}^{{\\rm P}} {{{\\bf E}}\\cdot {\\hbox{d}}{\\varvec l}}
	2.22 The Reference Point R in the Equation {\\hbox{V}} = - \\int\\limits_{{\\rm R}}^{{\\rm P}} {{{\\bf E}}\\cdot {\\hbox{d}}{\\varvec l}}
	2.22 The Reference Point R in the Equation {\\hbox{V}} = - \\int\\limits_{{\\rm R}}^{{\\rm P}} {{{\\bf E}}\\cdot {\\hbox{d}}{\\varvec l}}
	2.22 The Reference Point R in the Equation {\\hbox{V}} = - \\int\\limits_{{\\rm R}}^{{\\rm P}} {{{\\bf E}}\\cdot {\\hbox{d}}{\\varvec l}}
	2.22 The Reference Point R in the Equation {\\hbox{V}} = - \\int\\limits_{{\\rm R}}^{{\\rm P}} {{{\\bf E}}\\cdot {\\hbox{d}}{\\varvec l}}
	2.23 Poisson’s and Laplace’s Equation
	2.23 Poisson’s and Laplace’s Equation
	2.23 Poisson’s and Laplace’s Equation
	2.24 Conductors
	2.25 Boundary Conditions
	2.26 Uniqueness Theorem
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3 Electric Charges at Rest—Part II
	3.1 Work Done
	3.2 Energy in Electrostatic Fields
	3.3 Equipotential Surfaces
	3.4 A Note on Work Done
	3.4 A Note on Work Done
	3.4 A Note on Work Done
	3.4 A Note on Work Done
	3.4 A Note on Work Done
	3.4 A Note on Work Done
	3.4 A Note on Work Done
	3.5 Method of Images
	3.6 Point Charge Near a Grounded Conducting Sphere
	3.7 Laplace’s Equation—Separation of Variables
	3.8 Separation of Variables Laplace’s Equation in Cartesian Coordinates
	3.9 Potential Between Two Grounded Semi Infinite Parallel Electrodes Separated by a Plane Electrode Held by a Potential Vo
	3.10 Potential Between Two Grounded Conducting Electrodes Separated by Two Conducting Side Plates Maintained at Vo Potentials Vo and Vo
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.11 Separation of Variables—Laplace’s Equation in Spherical Polar Coordinates
	3.12 Separation of Variables—Laplace’s Equation in Cylindrical Coordinates
	3.12 Separation of Variables—Laplace’s Equation in Cylindrical Coordinates
	3.12 Separation of Variables—Laplace’s Equation in Cylindrical Coordinates
	3.12 Separation of Variables—Laplace’s Equation in Cylindrical Coordinates
	3.12 Separation of Variables—Laplace’s Equation in Cylindrical Coordinates
	3.13 Summary
	3.14 Dielectrics
	3.15 Dielectric in an Electric Field
	3.16 Polar and Non-Polar Molecules
	3.17 Potential Produced by the Polarized Dielectric
	3.18 Bound Charges {{\\varvec \\upsigma}}_{{{\\bf p}}} \\,{{\\bf and}}\\,{{\\varvec \\uprho}}_{{{\\bf p}}}
	3.19 Electric Displacement Vector and Gauss Law in Dielectrics
	3.20 Linear Dielectrics
	3.21 Dielectric Breakdown
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.22 Boundary Conditions in the Presence of Dielectrics
	3.23 Capacitance and Capacitors
	3.24 Principle of a Capacitor
		3.24.1 Capacity of a Parallel Plate Capacitor
		3.24.2 Capacity of a Parallel Plate Capacitor with Two Dielectrics
	3.25 Capacitance of a Spherical Capacitor
	3.26 Capacitance of a Cylindrical Capacitor
	3.27 Capacitors in Parallel and Series
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
	3.28 Energy Stored in a Capacitor
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4 Magnetostatics
	4.1 Introduction
	4.2 Lorentz Force Law
	4.3 Applications of Lorentz Force—Hall Effect
	4.4 Sources of Magnetic Field
	4.5 Magnetic Force Between Two Current Elements
	4.6 Biot–Savart Law
	4.7 Current Distributions
	4.8 Magnetic Flux Density Due to a Steady Current in a Infinitely Long Straight Wire
	4.9 Ampere’s Circuital Law
	4.10 Equation of Continuity
	4.11 The Divergence of B
	4.12 Magnetic Monopoles
	4.13 Magnetic Vector Potential
	4.14 Magnetic Scalar Potential
	4.15 Comments on Magnetic Vector Potential A and Magnetic Scalar Potential Vm
	4.16 B of a Current-Carrying Infinitely Long Straight Conductor
	4.17 B of a Current-Carrying Finite Straight Conductor
	4.18 B Along the Axis of the Current-Carrying Circular Loop
	4.19 B Inside a Long Solenoid
	4.20 B of a Toroid
	4.21 Summary
	4.22 Magnetic Dipole
	4.23 Magnetic Boundary Conditions
	4.24 Force Between Two Parallel Current-Carrying Conductors
	4.25 Torque on a Current Loop in a Uniform Magnetic Field
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
	4.26 Magnetic Flux
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5 Magnetic Fields in Materials
	5.1 Introduction
	5.2 Diamagnetism, Paramagnetism and Ferromagnetism
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	5.3 Magnetization: Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.4 Physical Interpretation of Bound Currents
	5.5 Magnetic Field and Ampere’s Law in Magnetized Materials
	5.6 Linear and Nonlinear Media
	5.6 Linear and Nonlinear Media
	5.6 Linear and Nonlinear Media
	5.7 Boundary Conditions
	5.7 Boundary Conditions
	5.7 Boundary Conditions
	5.7 Boundary Conditions
	5.7 Boundary Conditions
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6 Time-Varying Fields and Maxwell’s Equation
	6.1 Introduction—Ohm’s law
		6.1.1 Ohm’s law
	6.2 Electromotive Force
	6.3 Motional emf
	6.4 Faraday’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.5 Lenz’s Law
	6.6 Magnetic Circuits
	6.6 Magnetic Circuits
	6.6 Magnetic Circuits
	6.6 Magnetic Circuits
	6.6 Magnetic Circuits
	6.7 Induction—Self Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.8 Induction—Mutual Induction
	6.9 Energy Stored in the Circuit in Terms of Self-Inductance
	6.10 Energy Stored in Magnetic Fields
	6.10 Energy Stored in Magnetic Fields
	6.10 Energy Stored in Magnetic Fields
	6.10 Energy Stored in Magnetic Fields
	6.11 Maxwell’s Equation
	6.12 The Displacement Current
	6.13 Maxwell’s Equation in Matter
	6.14 Maxwell’s Equation in Integral Form and Boundary Conditions
	6.15 Potential Functions
	6.16 Gauge Transformations
	6.17 Retarded Potentials
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.18 Time-Harmonic Fields
	6.19 Maxwell’s Equation in Phasor Form
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7 Plane Electromagnetic Waves
	7.1 Introduction
	7.2 The Wave Equation
	7.3 Plane Electromagnetic Wave in Free Space
	7.3 Plane Electromagnetic Wave in Free Space
	7.3 Plane Electromagnetic Wave in Free Space
	7.4 Poynting Theorem
	7.5 Average Poynting Vector
	7.6 Poynting Vector for Wave Propagation in Free Space
	7.7 Plane Electromagnetic Waves in Lossy Dielectrics
	7.8 Plane Electromagnetic Waves in Good Conductors
	7.8 Plane Electromagnetic Waves in Good Conductors
	7.8 Plane Electromagnetic Waves in Good Conductors
	7.9 Plane Electromagnetic Waves in Lossy Dielectrics Using Maxwell’s Equation in Phasor Form
	7.10 Wave Polarization
	7.10 Wave Polarization
	7.10 Wave Polarization
	7.11 Reflection and Transmission of the Plane Wave at Normal Incidence
	7.12 Reflection and Transmission of the Plane Wave at Oblique Incidence
	7.13 Total Reflection and Total Transmission
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
	7.14 Dispersion—Group Velocity
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8 Transmission Lines
	8.1 Introduction
	8.2 Description of a Transmission Line
	8.3 Wave Propagation in a Transmission Line
	8.4 Transmission Line Equations
	8.5 Wave Propagation in the Transmission Line—Circuit Model
	8.6 Lossless Line
	8.7 Low-loss Line
	8.8 Distortionless Line
	8.9 Relationship Between G and C
	8.10 Determination of Transmission Line Parameters
	8.11 Field Approach—TEM Waves in a Parallel-Plate Transmission Line
	8.12 The Infinite Transmission Line
	8.13 Finite Transmission Line
	8.14 Standing Waves
	8.15 Lossless Transmission Lines with Resistive Transmission
	8.16 Smith Chart
	8.17 Impedance Matching
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9 Waveguides
	9.1 Introduction
	9.2 Transverse Electromagnetic, Transverse Electric and Transverse Magnetic Waves
	9.3 Wave Equation in Cartesian Coordinates
	9.4 Parallel-Plate Waveguide
	9.4 Parallel-Plate Waveguide
	9.5 Propagation of TEM, TE and TM Waves in Parallel-Plate Waveguide
	9.5 Propagation of TEM, TE and TM Waves in Parallel-Plate Waveguide
	9.5 Propagation of TEM, TE and TM Waves in Parallel-Plate Waveguide
	9.6 General Solution of Wave Equation
	9.7 Rectangular Waveguides
	9.7 Rectangular Waveguides
	9.7 Rectangular Waveguides
	9.7 Rectangular Waveguides
	9.7 Rectangular Waveguides
	9.7 Rectangular Waveguides
	9.7 Rectangular Waveguides
	9.8 Cavity Resonators
	9.9 Quality Factor
	9.9 Quality Factor
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10 Antennas
	10.1 Introduction
	10.2 Types of Antenna
	10.3 Hertzian Dipole
	10.4 Magnetic Dipole
	10.5 Half Wave Dipole Antenna
	10.6 Antenna Arrays
	10.7 Receiving Antenna and Friis Equation
	10.8 The Radar Equation
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