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# Engineering Electromagnetics by Nathan Ida

## Contents of Engineering Electromagnetics eBook

• Vector Algebra
• Introduction
• Scalars and Vectors
• Magnitude and Direction of Vectors: The Unit Vector
• and Components of a Vector
• Vector Scaling
• Products of Vectors
• The Scalar Product
• The Vector Product
• Multiple Vector and Scalar Products
• Definition of Fields
• Scalar Fields
• Vector Fields
• Systems of Coordinates
• The Cartesian Coordinate System
• The Cylindrical Coordinate System
• The Spherical Coordinate System
• Transformation from Cylindrical to Spherical Coordinates
• Position Vectors
• Problems
• Vector Calculus
• Introduction
• Integration of Scalar and Vector Functions
• Line Integrals
• Surface Integrals
• Volume Integrals
• Differentiation of Scalar and Vector Functions
• The Gradient of a Scalar Function
• The Divergence of a Vector Field
• The Divergence Theorem
• Circulation of a Vector and the Curl
• Stokes’ Theorem
• Conservative and Nonconservative Fields
• Null Vector Identities and Classification of Vector Fields
• The Helmholtz Theorem
• Second-Order Operators
• Other Vector Identities
• Problems
• Coulomb’s Law and the Electric Field
• Introduction
• Charge and Charge Density
• Coulomb’s Law
• The Electric Field Intensity
• Electric Fields of Point Charges
• Electric Fields of Charge Distributions
• The Electric Flux Density and Electric Flux
• Applications
• Experiments
• Summary
• Problems
• Gauss’s Law and the Electric Potential
• Introduction
• The Electrostatic Field: Postulates
• Gauss’s Law
• Applications of Gauss’s Law
• The Electric Potential
• Electric Potential Due to Point Charges
• Electric Potential Due to Distributed Charges
• Calculation of Electric Field Intensity from Potential
• Materials in the Electric Field
• Conductors
• Dielectric Materials
• Polarization and the Polarization Vector
• Electric Flux Density and Permittivity
• Dielectric Strength
• Interface Conditions
• Interface Conditions Between Two Dielectrics
• Interface Conditions Between Dielectrics and Conductors
• Capacitance
• The Parallel Plate Capacitor
• Capacitance of Infinite Structures
• Connection of Capacitors
• Energy in the Electrostatic Field: Point and Distributed Charges
• Energy in the Electrostatic Field: Field Variables
• Forces in the Electrostatic Field: The Principle of Virtual Work
• Applications
• Experiments
• Summary
• Problems
• Boundary Value Problems: Analytic Methods of Solution
• Introduction
• Poisson’s Equation for the Electrostatic Field
• Laplace’s Equation for the Electrostatic Field
• Solution Methods
• Uniqueness of Solution
• Solution by Direct Integration
• The Method of Images
• Separation of Variables: Solution to Laplace’s Equation
• Experiments: The Method of Images
• Summary
• Problems
• Boundary Value Problems: Numerical (Approximate) Methods
• Introduction
• A Note on Computer Programs
• The General Idea of Numerical Solutions
• The Finite Difference Method: Solution to the Laplace
• and Poisson Equations
• The Finite Difference Approximation: First-Order Derivative
• The Finite Difference Approximation: Second-Order Derivative
• Implementation
• Solution to Poisson’s Equation
• The Method of Moments: An Intuitive Approach
• The Finite Element Method: Introduction
• The Finite Element
• Implementation of the Finite Element Method
• Summary
• Problems
• Introduction
• Conservation of Charge
• Conductors, Dielectrics, and Lossy Dielectrics
• Moving Charges in an Electric Field
• Convection Current and Convection Current Density
• Conduction Current and Conduction Current Density
• Ohm’s Law
• Power Dissipation and Joule’s Law
• The Continuity Equation and Kirchhoff’s Current Law
• Kirchhoff’s Current Law
• Current Density as a Field
• Kirchhoff’s Voltage Law
• Interface Conditions for Current Density
• Applications
• Experiments
• Summary
• Problems
• The Static Magnetic Field
• Introduction
• The Magnetic Field, Magnetic Field Intensity,
• and Magnetic Flux Density
• The Biot–Savart Law
• Applications of the Biot–Savart Law to Distributed Currents
• Ampere’s Law
• Magnetic Flux Density and Magnetic Flux
• Postulates of the Static Magnetic Field
• Potential Functions
• The Magnetic Vector Potential
• The Magnetic Scalar Potential
• Applications
• Experiments
• Summary
• Problems
• Magnetic Materials and Properties
• Introduction
• Magnetic Properties of Materials
• The Magnetic Dipole
• Magnetization: A Model of Magnetic Properties of Materials
• Behavior of Magnetic Materials
• Magnetic Interface Conditions
• Interface Conditions for the Tangential and Normal
• Components of the Magnetic Field Intensity H
• Inductance and Inductors
• Inductance per Unit Length
• External and Internal Inductance
• Energy Stored in the Magnetic Field
• Magnetostatic Energy in Terms of Fields
• Magnetic Circuits
• Forces in the Magnetic Field
• Principle of Virtual Work: Energy in a Gap
• Torque
• Applications
• Experiments
• Summary
• Problems
• Introduction
• Lenz’s Law
• Motional Electromotive Force: The DC Generator
• Induced emf Due to Transformer Action
• Combined Motional and Transformer Action
• Electromotive Force
• The Alternating Current Generator
• The Transformer
• The Ideal Transformer
• The Real Transformer: Finite Permeability
• The Real Transformer: Finite Permeability and Flux Leakage
• Eddy Currents
• Applications
• Experiments
• Summary
• Problems
• Maxwell’s Equations
• Introduction: The Electromagnetic Field
• Maxwell’s Equations
• Maxwell’s Equations in Differential Form
• Maxwell’s Equations in Integral Form
• Time-Dependent Potential Functions
• Scalar Potentials
• The Magnetic Vector Potential
• Other Potential Functions
• Interface Conditions for the Electromagnetic Field
• Interface Conditions for the Electric Field
• Interface Conditions for the Magnetic Field
• Particular Forms of Maxwell’s Equations
• Time-Harmonic Representation
• Maxwell’s Equations: The Time-Harmonic Form
• Source-Free Equations
• Summary
• Problems
• Electromagnetic Waves and Propagation
• Introduction
• The Wave
• The Electromagnetic Wave Equation and Its Solution
• The Time-Dependent Wave Equation
• Time-Harmonic Wave Equations
• Solution of the Wave Equation
• Solution for Uniform Plane Waves
• The One-Dimensional Wave Equation in Free-Space and Perfect Dielectrics
• The Electromagnetic Spectrum
• The Poynting Theorem and Electromagnetic Power
• The Complex Poynting Vector
• Propagation of Plane Waves in Materials
• Propagation of Plane Waves in Lossy Dielectrics
• Propagation of Plane Waves in Low-Loss Dielectrics
• Propagation of Plane Waves in Conductors
• The Speed of Propagation of Waves and Dispersion
• Polarization of Plane Waves
• Linear Polarization
• Elliptical and Circular Polarization
• Applications
• Experiments
• Summary
• Problems
• Reflection and Transmission of Plane Waves
• Introduction
• Reflection and Transmission at a General Dielectric Interface:
• Normal Incidence
• Reflection and Transmission at an Air-Lossy Dielectric
• Interface: Normal Incidence
• Reflection and Transmission at an Air-Lossless Dielectric
• Interface: Normal Incidence
• Reflection and Transmission at an Air-Conductor Interface:
• Normal Incidence
• Reflection and Transmission at an Interface: Oblique Incidence on a Conductor
• Oblique Incidence on a Conducting Interface:
• Perpendicular Polarization
• Oblique Incidence on a Conducting Interface:
• Parallel Polarization
• Oblique Incidence on Dielectric Interfaces
• Oblique Incidence on a Dielectric Interface: Perpendicular
• Polarization
• Oblique Incidence on a Dielectric Interface:
• Parallel Polarization
• Brewster’s Angle
• Total Reflection
• Reflection and Transmission for Layered Materials at Normal Incidence
• Applications
• Experiments
• Summary
• Problems
• Theory of Transmission Lines
• Introduction
• The Transmission Line
• Transmission Line Parameters
• Calculation of Line Parameters
• The Transmission Line Equations
• Time-Domain Transmission Line Equations
• Types of Transmission Lines
• The Lossless Transmission Line
• The Long Transmission Line
• The Distortionless Transmission Line
• The Low-Resistance Transmission Line
• The Field Approach to Transmission Lines
• Finite Transmission Lines
• Line Impedance and the Generalized
• Reflection Coefficient
• The Lossless, Terminated Transmission Line
• The Lossless, Matched Transmission Line
• The Lossless, Shorted Transmission Line
• The Lossless, Open Transmission Line
• The Lossless, Resistively Loaded Transmission Line
• Power Relations on a General Transmission Line
• Resonant Transmission Line Circuits
• Applications
• Experiment
• Summary
• Problems
• The Smith Chart, Impedance Matching, and Transmission
• Line Circuits
• Introduction
• The Smith Chart
• The Smith Chart as an Admittance Chart
• Impedance Matching and the Smith Chart
• Impedance Matching
• Stub Matching
• Quarter-Wavelength Transformer Matching
• Experiments
• Summary
• Problems
• Transients on Transmission Lines
• Introduction
• Propagation of Narrow Pulses on Finite, Lossless
• Transmission Lines
• Propagation of Narrow Pulses on Finite, Distortionless
• Transmission Lines
• Transients on Transmission Lines: Long Pulses
• Transients on Transmission Lines: Finite-Length Pulses
• Reflections from Discontinuities
• Initial Conditions on Transmission Lines
• Experiments
• Summary
• Problems
• Waveguides and Resonators
• Introduction
• The Concept of a Waveguide
• Transverse Electromagnetic, Transverse Electric,
• and Transverse Magnetic Waves
• Transverse Electromagnetic Waves
• Transverse Electric (TE) Waves
• Transverse Magnetic (TM) Waves
• TE Propagation in Parallel Plate Waveguides
• TM Propagation in Parallel Plate Waveguides
• TEM Waves in Parallel Plate Waveguides
• Rectangular Waveguides
• TM Modes in Rectangular Waveguides
• TE Modes in Rectangular Waveguides
• Attenuation and Losses in Rectangular Waveguides
• Other Waveguides
• Cavity Resonators
• TM Modes in Cavity Resonators
• TE Modes in Cavity Resonators
• Energy Relations in a Cavity Resonator
• Quality Factor of a Cavity Resonator
• Applications
• Summary
• Problems
• Introduction
• Antennas
• The Electric Dipole
• The Near Field
• The Far Field
• Properties of Antennas
• Antenna Directivity
• Antenna Gain and Radiation Efficiency
• The Magnetic Dipole
• Near Fields for the Magnetic Dipole
• Far Fields for the Magnetic Dipole
• Properties of the Magnetic Dipole
• Practical Antennas
• Linear Antennas of Arbitrary Length
• The Monopole Antenna
• Antenna Arrays
• The Two-Element Array
• The n-Element Linear Array
• Reciprocity and Receiving Antennas
• Effective Aperture