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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!

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)

Contents

ISBN 13: 9781891121463 ISBN 189112146-4

SciTech Publishing, Inc. Raleigh, NC

www.scitechpub.com 9

781891

121463

2008+

Solved Problems in Electromagnetics

Syed A. Nasar

Vector Analysis, Electrostatics, Magnetostatics, Maxwell’s Equations, Plane Waves, Transmission Lines, Waveguides, Cavity Resonators, Antennas, Review Problems

2008+ Solved Problems in Electromagnetics

2008+ Solved Problems in Electromagnetics

Syed A. Nasar

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 ISBN 13: 9781891121463

CONTENTS Chapter 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

Chapter 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

Chapter 3

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

Chapter 4

MAXW 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

Chapter 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

Chapter 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

Chapter 7

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

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

Chapter 9

ANTENNAS

327

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 10 INDEX

REVIEW PROBLEMS

376 437

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!

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)

Contents

ISBN 13: 9781891121463 ISBN 189112146-4

SciTech Publishing, Inc. Raleigh, NC

www.scitechpub.com 9

781891

121463

2008+

Solved Problems in Electromagnetics

Syed A. Nasar

Vector Analysis, Electrostatics, Magnetostatics, Maxwell’s Equations, Plane Waves, Transmission Lines, Waveguides, Cavity Resonators, Antennas, Review Problems

2008+ Solved Problems in Electromagnetics

2008+ Solved Problems in Electromagnetics

Syed A. Nasar

View more...
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)

Contents

ISBN 13: 9781891121463 ISBN 189112146-4

SciTech Publishing, Inc. Raleigh, NC

www.scitechpub.com 9

781891

121463

2008+

Solved Problems in Electromagnetics

Syed A. Nasar

Vector Analysis, Electrostatics, Magnetostatics, Maxwell’s Equations, Plane Waves, Transmission Lines, Waveguides, Cavity Resonators, Antennas, Review Problems

2008+ Solved Problems in Electromagnetics

2008+ Solved Problems in Electromagnetics

Syed A. Nasar

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 ISBN 13: 9781891121463

CONTENTS Chapter 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

Chapter 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

Chapter 3

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

Chapter 4

MAXW 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

Chapter 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

Chapter 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

Chapter 7

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

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

Chapter 9

ANTENNAS

327

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 10 INDEX

REVIEW PROBLEMS

376 437

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!

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)

Contents

ISBN 13: 9781891121463 ISBN 189112146-4

SciTech Publishing, Inc. Raleigh, NC

www.scitechpub.com 9

781891

121463

2008+

Solved Problems in Electromagnetics

Syed A. Nasar

Vector Analysis, Electrostatics, Magnetostatics, Maxwell’s Equations, Plane Waves, Transmission Lines, Waveguides, Cavity Resonators, Antennas, Review Problems

2008+ Solved Problems in Electromagnetics

2008+ Solved Problems in Electromagnetics

Syed A. Nasar

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