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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: 9781891121463

SciTech 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

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d Pr

oblems in Elect

romagnet

ics

Sye

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. N

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ar

(2)

2008

+

Solved Problems in

ELECTROMAGNETICS

Syed A. Nasar, Ph.D.

Raleigh, North Carolina

www.scitechpub.com

(3)

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

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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

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iv

a

CONTENTS

Chapter 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

Chapter 9 ANTENNAS

327

Chapter 10 REVIEW PROBLEMS

376

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