Author: Masud Mansuripur

Field, Force, Energy and Momentum in Classical Electrodynamics (Revised Edition)

eBook: US $99 Special Offer (PDF + Printed Copy): US $307
Printed Copy: US $258
Library License: US $396
ISBN: 978-1-68108-557-9 (Print)
ISBN: 978-1-68108-556-2 (Online)
Year of Publication: 2017
DOI: 10.2174/97816810855621170101


The classical theory of electrodynamics is based on Maxwell's equations and the Lorentz law of force. This book begins with a detailed analysis of these equations, and proceeds to examine their far-reaching consequences. The traditional approach to electrodynamics treats the ‘microscopic’ equations of Maxwell as fundamental, with electric charge and electric current as the sole sources of the electric and magnetic fields. Subsequently, polarization and magnetization are introduced into Maxwell's equations to account for the observed behavior of material media. The augmented equations, known as Maxwell's ‘macroscopic’ equations, are considered useful for practical applications, but are also ultimately reducible to the more fundamental ‘microscopic’ equations. In contrast, this textbook treats Maxwell's ‘macroscopic’ equations as the foundation of classical electrodynamics, and treats electrical charge, electrical current, polarization, and magnetization as the basic constituents of material media. The laws that govern the distribution of electromagnetic energy and momentum in space-time are also introduced in an early chapter, then discussed in great detail in subsequent chapters.

The text presents several examples that demonstrate the solution of Maxwell's equations in diverse situations, aiming to enhance the reader’s understanding of the flow of energy and momentum as well as the distribution of force and torque throughout the matter-field systems under consideration.

This revised edition of Field, Force, Energy and Momentum in Classical Electrodynamics features revised chapters, some of which include expanded discussions of fundamental concepts or alternative derivations of important formulas. The new edition also features three additional chapters covering Maxwell’s equations in spherical coordinates (Chapter 10), the author’s recent discussion (and streamlined proof) of the Optical Theorem (Chapter 13), and the fascinating connections between electromagnetism and Einstein’s special theory of relativity (Chapter 15). A new appendix covers the SI system of units that has been used throughout the book.

The book is a useful textbook for physics majors studying classical electrodynamics. It also serves as a reference for industry professionals and academic faculty in the fields of optics and advanced electronics.


It has now been nearly six years since the publication of the first edition of Field, Force, Energy and Momentum in Classical Electrodynamics. In the intervening years, I have continued to teach my electrodynamics course to the incoming class of graduate students at the University of Arizona’s College of Optical Sciences. This one-semester course, which is based on the first seven chapters of the present book, covers the fundamental aspects of the Maxwell-Lorentz theory of electromagnetism, aiming to prepare the students for advanced studies in the various subfields of Optics and Photonics. Each year, I have had to come up with new problem sets to assign as homework or to ask during examinations. The new problems are now added at the end of the relevant chapters. Solutions to problems marked with an asterisk (*) appear in the back of the book under the heading Solutions to Selected Problems.

Also appearing for the first time in this revised edition are the following three chapters: Chapter 10 on Maxwell’s Equations in Spherical Coordinates, Chapter 13 on the Optical Theorem, and Chapter 15 on Electromagnetism and Special Relativity. A new appendix provides an in-depth coverage of the International System of Units (SI), which is used throughout the book. In addition, Chapter 6 has been revised to include an alternative derivation of the Kramers-Kronig relations, while Chapter 9 has been expanded to include discussions of trapped light in cylindrical cavities, electromagnetic angular momentum, and Mie scattering from cylindrical objects. Several other chapters have also undergone revisions and adjustments.

All in all, Chapters 1-9, 11, 12 and 14 are derived, in whole or in part, from Chapters 1-12 published in the previous edition of the present e-book. Chapters 13 and 14 are based on my previously published papers in the American Journal of Physics and Optics Communications, respectively. These publications are cited in the footnotes appearing at the end of each chapter. The material in the rest of the book is original and has not been published elsewhere. I hereby declare that the entire book is free from conflicts of interest.

It is my sincere hope that the old material as well as the new features appearing in this revised edition will provide the reader with a broad perspective on the many fascinating aspects of the classical theory of electrodynamics.


For their thoughtful comments and questions, as well as suggestions that have resulted in significant improvements over the first edition, I am grateful to numerous students who have taken my electrodynamics course during the past six years.

Conflict of Interest:

The author declares no conflict of interest, financial or otherwise.

Tucson, June 2017
Masud Mansuripur


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