2008+ Solved Problems in Electromagnetics
Table of Contents
1 Vector Analysis
Vectors and Scalars
Unit Vectors
Scalar Components and Vector Components
Vectorial Areas
Dot Product
Cross Product
Vector Fields and Scalar Fields
The Gradient Vector
Line Integrals
Divergence and the Divergence Theorem
Curl and Stokes’ Theorem
Potential Functions and Conservative Fields
2 Electrostatics
Charge Distributions
Coulomb’s Law
The E-Field
Superposition Principle
Electric Flux and Gauss’ Law
Induced Charge
Voltage
Electric Dipoles
Dielectrics and Polarization
Permittivity
Conditions at an Interface
Potential Energy of a Charge Configuration
Equipotentials and Field Lines
Capacitance
Poisson’s and Laplace’s Equations
Solutions by Separation of Variables
Method of Images
3 Magnetostatics
Ampère’s Force Law
Biot-Savart Law
Magnetic Induction
Magnetic Field Intensity
Ampère’s Circuital Law
Magnetic Flux
Magnetic Dipole Moments
Torque on a Current Loop
Magnetic Vector and Scalar Potentials
Conditions at an Interface
Bound Currents and Magnetization
The Lorentz Force
Magnetic Circuits
Mutual Inductance
Internal Inductance
Magnetostatic Force
4 Maxwell's Equations
Faraday’s Law of Induced EMF
Lenz’s Law
Displacement Current
Point and Integral Forms of Maxwell’s Equations
Phasor Notation
The Poynting Vector and Radiated Power
Derivation of Wave Equations and Diffusion Equations
Special Solutions in Conductors; Definitions of Skin Depth and Internal Impedance
5 Plane Waves
The Helmholtz Equation and Its Plane Wave Solutions
Propagation Constant, Wavelength, Phase Velocity, Intrinsic Impedance
Time-Average Poynting Vector
The Loss Tangent
Approximations for the Propagation Constant and Intrinsic Impedance
Wave Polarization
Group Velocity and Dispersion
Reflection and Transmission at an Interface
Crank Diagram
Standing Waves
Perpendicular and Parallel Polarizations
Laws of Reflection and Refraction
Fresnel Equations
The Brewster Angle
6 Transmission Lines
TEM Field Structure
The (Lossless) Transmission-Line Equations
Propagation Velocity and Characteristic Resistance
Voltage and Current Reflection
Steady-State Analysis
Complex Voltage Reflection Coefficient; Input Impedance; Electrical Length
Crank Diagram
VSWR
Electrically Short Lines
The (Lossy) Transmission-Line Equations
Propagation Constant and Characteristic Impedance
Per-Unit-Length-Parameters
Normalized Impedance and the Smith Chart
7 Waveguides
Lossless Rectangular Guides: the Wave Equation
TE and TM Solutions
Cutoff Frequencies
Field Lines
Dominant Mode
Average Power Flow
Lossy Guides: Core and Wall Losses
Cylindrical Waveguides: Maxwell’s Equations
Bessel Function Solutions for TM and TE Modes
Dielectric-Slab Waveguides
Optical Fibers
8 Cavity Resonators
Field Equations for Rectangular Cavities
Resonant Frequencies
Energy Storage, Losses, and the Quality Factor
Coaxial Cavities
Equivalent-Circuit Parameters
Cylindrical Cavities
Spherical Cavities
9 Antennas
The Hertzian Dipole
Properties of the Far Field
Power or Radiation Pattern
Radiation Resistance
The Magnetic Dipole
Finite (Lossless) Dipole Antennas
The Angle Factor
Input Impedance
Lossy Dipole Antennas
Radiative Efficiency
Antenna Arrays
Principle of Pattern Multiplication
Radiation Intensity, Directive Gain, and Directivity
Coupled Antennas: Equivalent Circuits and the Reciprocity Theorem
Effective Aperture of an Antenna
(Power) Gain
The Friis Transmission Equation
Effects of a Ground Plane
Beam Solid Angle
Effective Antenna Length
Diffraction Patterns
Polarization Loss Factor (PLF)
HPBW and BWFN
Hansen-Woodyard Criteria
10 Review Problems
Index