1st Edition

Electromagnetic Boundary Problems

ISBN 9781498730266
Published October 15, 2015 by CRC Press
341 Pages 8 Color & 63 B/W Illustrations

USD $180.00

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Book Description

Electromagnetic Boundary Problems introduces the formulation and solution of Maxwell’s equations describing electromagnetism. Based on a one-semester graduate-level course taught by the authors, the text covers material parameters, equivalence principles, field and source (stream) potentials, and uniqueness, as well as:

  • Provides analytical solutions of waves in regions with planar, cylindrical, spherical, and wedge boundaries
  • Explores the formulation of integral equations and their analytical solutions in some simple cases
  • Discusses approximation techniques for problems without exact analytical solutions
  • Presents a general proof that no classical electromagnetic field can travel faster than the speed of light
  • Features end-of-chapter problems that increase comprehension of key concepts and fuel additional research

Electromagnetic Boundary Problems uses generalized functions consistently to treat problems that would otherwise be more difficult, such as jump conditions, motion of wavefronts, and reflection from a moving conductor. The book offers valuable insight into how and why various formulation and solution methods do and do not work.

Table of Contents

List of Figures

List of Tables


Author Bios

Maxwell's Equations and Sources

Maxwell Equations in Free Space

Energy Transfer and Poynting's Theorem

Macroscopic Maxwell Equations in Material Media

Multipole Expansions for Charges and Currents

Averaging of Charge and Current Densities

Conduction, Polarization, and Magnetization

Time-Harmonic Problems

Duality; Equivalence; Surface Sources

Duality and Magnetic Sources

Stream Potentials

Equivalence Principles

Jump Conditions

General Jump Conditions at a Stationary Surface

Example: Thin-Sheet Boundary Conditions

Jump Conditions at a Moving Surface

Force on Surface Sources

Example: Charge Dipole Sheet at a Dielectric Interface


Potential Representations of the Electromagnetic Field

Lorenz Potentials and their Duals (A, Φ, F, Ψ)

Hertz Vector Potentials

Jump Conditions for Hertz Potentials

Time-Harmonic Hertz Potentials

Special Hertz Potentials

Whittaker Potentials

Debye Potentials


Fundamental Properties of the Electromagnetic Field

Causality; Domain of Dependence

Domain of Dependence

Motion of Wavefronts

The Ray Equation and the Eikonal

Passivity and Uniqueness

Time-Domain Theorems

Radiation Conditions

Time-Harmonic Theorems

Equivalence Principles and Image Theory

Lorentz Reciprocity

Scattering Problems

Aperture Radiation Problems

Classical Scattering Problems

Aperture Scattering Problems

Planar Scatterers and Babinet's Principle


Radiation by Simple Sources and Structures

Point and Line Sources in Unbounded Space

Static Point Charge

Potential of a Pulsed Dipole in Free Space

Time-Harmonic Dipole

Line Sources in Unbounded Space

Alternate Representations for Point and Line Source Potentials

Time-Harmonic Line Source

Time-Harmonic Point Source

Radiation from Sources of Finite Extent; The Fraunhofer Far Field Approximation

Far Field Superposition

Far Field via Fourier Transform

The Stationary Phase Principle

Radiation in Planar Regions

The Fresnel and Paraxial Approximations; Gaussian Beams

The Fresnel Approximation

The Paraxial Approximation

Gaussian Beams


Scattering by Simple Structures

Dipole Radiation over a Half-Space

Reflected Wave in the Far Field

Transmitted Wave in the Far Field

Other Dipole Sources

Radiation and Scattering from Cylinders

Aperture Radiation

Plane Wave Scattering

Diffraction by Wedges; The Edge Condition


The Edge Condition

Formal Solution of the Problem

The Geometrical Optics Field

The Diffracted Field

Uniform Far-Field Approximation

Spherical Harmonics


Propagation and Scattering in More Complex Regions

General Considerations


Parallel-Plate Waveguide: Mode Expansion

Parallel-Plate Waveguide: Fourier Expansion

Open Waveguides

Propagation in a Periodic Medium

Gel'fand's Lemma

Bloch Wave Modes and Their Properties

The Bloch Wave Expansion

Solution for the Field of a Current Sheet in Terms of Bloch Modes


Integral Equations in Scattering Problems

Green's Theorem and Green's Functions

Scalar Problems

Vector Problems

Dyadic Green's Functions

Relation to Equivalence Principle

Integral Equations for Scattering by a Perfect Conductor

Electric-Field Integral Equation (EFIE)

Magnetic-Field Integral Equation (MFIE)

Nonuniqueness and Other Difficulties

Volume Integral Equations for Scattering by a Dielectric Body

Integral Equations for Static "Scattering" by Conductors

Electrostatic Scattering

Magnetostatic Scattering

Electrostatics of a Thin Conducting Strip

Electrostatics of a Thin Conducting Circular Disk

Integral Equations for Scattering by an Aperture in a Plane

Static Aperture Problems

Electrostatic Aperture Scattering

Magnetostatic Aperture Scattering

Example: Electric Polarizability of a Circular Aperture


Approximation Methods

Recursive Perturbation Approximation

Example: Strip over a Ground Plane

Physical Optics Approximation

Operator Formalism for Approximation Methods

Example: Strip over a Ground Plane (Revisited)

Variational Approximation

The Galerkin-Ritz Method

Example: Strip over a Ground Plane (Re-Revisited)


Appendix A: Generalized Functions


Multiplication of Generalized Functions

Fourier Transforms and Fourier Series of Generalized Functions

Multidimensional Generalized Functions


Appendix B: Special Functions

Gamma Function

Bessel Functions

Spherical Bessel Functions

Fresnel Integrals

Legendre Functions

Chebyshev Polynomials

Exponential Integrals



Appendix C: Rellich's Theorem

Appendix D: Vector Analysis

Vector Identities

Vector Differentiation in Various Coordinate Systems

Rectangular (Cartesian) Coordinates

Circular Cylindrical Coordinates

Spherical Coordinates

Poincaré's Lemma

Helmholtz’s Theorem

Generalized Leibnitz Rule



Appendix E: Formulation of Some Special Electromagnetic Boundary Problems

Linear Cylindrical (Wire) Antennas

Transmitting Mode

Receiving Mode

Static Problems

Electrostatic Problems

The Capacitance Problem

The Electric Polarizability Problem

Magnetostatic Problems

The Inductance Problem

The Magnetic Polarizability Problem



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Edward F. Kuester received a BS degree from Michigan State University, East Lansing, USA, and MS and Ph.D degrees from the University of Colorado Boulder (UCB), USA, all in electrical engineering. Since 1976, he has been with the Department of Electrical, Computer, and Energy Engineering at UCB, where he is currently a professor. He also has been a summer faculty fellow at the Jet Propulsion Laboratory, Pasadena, California, USA; visiting professor at the Technische Hogeschool, Delft, The Netherlands; invited professor at the École Polytechnique Fédérale de Lausanne, Switzerland; and visiting scientist at the National Institute of Standards and Technology (NIST), Boulder, Colorado, USA. Widely published, Dr. Kuester is a fellow of the Institute of Electrical and Electronics Engineers (IEEE), and a member of the Society for Industrial and Applied Mathematics (SIAM) and Commissions B and D of the International Union of Radio Science (URSI).

David C. Chang holds a bachelor's degree in electrical engineering from National Cheng Kung University, Tainan, Taiwan, and MS and Ph.D degrees in applied physics from Harvard University, Cambridge, Massachusetts, USA. He was previously full professor of electrical and computer engineering at the University of Colorado Boulder (UCB), USA, where he also served as chair of the department and director of the National Science Foundation Industry/University Cooperative Research Center for Microwave/Millimeter-Wave Computer-Aided Design. He then became dean of engineering and applied sciences at Arizona State University, Tempe, USA; was named president of Polytechnic University (now the New York University Polytechnic School of Engineering (NYU Poly)), Brooklyn, USA; and was appointed as NYU Poly chancellor. He retired from that position in 2013, and is now professor emeritus at the same university. Dr. Chang is a life fellow of the Institute of Electrical and Electronics Engineers (IEEE); stays active in the International Scientific Radio Union (URSI); has been named an honorary professor at five major Chinese universities; serves as chairman of the International Board of Advisors at Hong Kong Polytechnic University, Hung Hom; and was appointed special advisor to the president of Nanjing University, China.


"… a unique title by two authors whose in-depth knowledge of this material and ability to present it to others are hardly matched. While the book provides distinguishing coverage and presentation of many topics, some discussions cannot be found elsewhere. I highly recommend this outstanding piece, bringing great value as both a textbook and reference text."
—Branislav M. Notaros, Colorado State University, Fort Collins, USA

"… useful for students, researchers, engineers, and teachers of electromagnetics. Today, in many universities, this discipline is taught by teachers who do not have much research experience in electromagnetism. That is why this textbook, written by world-known specialists and showing how electromagnetics courses should be built and taught, is very important. The authors have made clearer several aspects of electromagnetism which are poorly highlighted in earlier-published literature."
—Guennadi Kouzaev, Norwegian University of Science and Technology, Trondheim

"Graduate students and learners of electromagnetics of any age and status: If you have not had a chance to attend graduate-level courses taught by great professors like Edward F. Kuester and David C. Chang, here comes opportunity knocking on your door. Electromagnetic Boundary Problems is borne out of course notes prepared, used, corrected, and perfected by the authors over the years at the University of Colorado, Boulder. This is a book of gems."
IEEE Antennas and Propagation, October 2016