2008+
Solved Problems in
Electromagnetics
Syed A. Nasar
9 7 8 1 8 9 1 1 2 1 4 6 3 ISBN 189112146-4 ISBN 13: 9781891121463SciTech Publishing, Inc.
Raleigh, NC
www.scitechpub.com
2008+ Solved Problems
in Electromagnetics
by Syed A. Nasar
About the book
SciTech Publishing is reissuing this extremely
valuable learning resource, originally published
in 1992 in the Schaum’s Problem-Solving Series
for students of electromagnetics and those who
wish to refresh and solidify their understanding
of its challenging applications. Problem-solving
drills help develop confidence, but few
textbooks offer the answers – never mind the
complete solutions – to their chapter exercises.
Here, noted author Professor Syed Nasar has
divided the book’s problems into topic areas
similar to a textbook and presented a wide
array of problems, followed immediately by
their solutions.
– Learn the best strategies for solving tough
problems in step-by-step detail
– Prepare effectively for exams
– Use the Index to quickly locate the type of
problems you need to review
– Save and use again for refresher
– Instructors: this is a great source for extra
homework, quizzes, and exams!
Contents
Vector Analysis, Electrostatics, Magnetostatics,
Maxwell’s Equations, Plane Waves, Transmission
Lines, Waveguides, Cavity Resonators,
Antennas, Review Problems
Also of interest from sCiteCh Publishing:
› Fundamentals of Electromagnetics with MATLAB
®,
2nd Edition, by Karl Lonngren, Sava Savov, Randy Jost
Employing the power of MATLAB as both a
visualization and a problem-solving tool, this book
teaches electromagnetics in a much more engaging
manner than traditional textbooks.
(ISBN13: 9781891121588)
› Antenna Design and Visualization Using MATLAB
®,
by Atef Elsherbeni and Matthew Inman
This software program comes with a 110-page User
Guide in a PDF file. It helps students and engineers
in antenna design see the changes resulting from
alterations to the parameters of design specifications.
The authors’ website provides free upgrades and help
to all who purchase and register the product.
(ISBN13: 9781891121395)
› Electronic Applications of the Smith Chart,
by Phillip Smith
The legendary Smith chart inventor’s classic reference
book describes how the chart is used for designing
lumped element and transmission line circuits. It
provides tutorial material on transmission line
theory and behavior, circuit representation on the
chart, matching networks, network transformations
and broadband matching. It also includes a new
chapter with examples designs and description of the
winSMITH software accessory.
(ISBN13: 9781884932397)
2008+ Sol
ve
d Pr
oblems in Elect
romagnet
ics
Sye
d A
. N
as
ar
2008
+
Solved Problems in
ELECTROMAGNETICS
Syed A. Nasar, Ph.D.
Raleigh, North Carolina
www.scitechpub.com
SciTech Publishing, Inc.
911 Paverstone Drive, Suite B
Raleigh, NC 27615
Phone: 919-847-2434 Fax: 919-847-2568
www.scitechpub.com
Editor: Dudley R. Kay
Production Director: Susan Manning
Production Assistant: Robert Lawless
Cover design by Kathy Gagne
Cover image courtesy of Greg Shirah of NASA,
http://pwg.gsfc.nasa.gov/istp/outreach/images/Aurora/71300.jpg
Copyright 2008 by SciTech Publishing, Inc.
All rights reserved. No part of this book may be reproduced in any
form or by any means without prior written permission of the publisher.
First edition published as 2000 Solved Problems in Electromagnetics
copyright 1992 by McGraw-Hill.
Printed in the United States of America.
ISBN: 1891121464
CONTENTS
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
VECTO R 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
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
M AGNETOST ATICS
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
M AXW ELL’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
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
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
W AVEGUIDES
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
iv
a
CONTENTSChapter 8 CAVITY RESONATORS
307
Field Equations for Rectangular Cavities / Resonant Frequencies / Energy Storage, Losses, and the Quality Factor / Coaxial Cavities / Equivalent-Circuit
Parameters / Cylindrical Cavities / Spherical Cavities
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