Understanding the Electromagnetic Field

Understanding the Electromagnetic Field is an entry level textbook for graduate students with a focus on the electromagnetic field. This book explores the relationship between the field and electric charges.

The earlier part of the book deals with the derivation of Maxwell's equations from experimental laws. Next, the electromagnetic field is studied in the light of special relativity, leading logically to the quantum theory of radiation. Quantum mechanics is introduced as a quantum field theory of the electromagnetic field. The rules of quantum mechanics are developed in a systematic way, with relativistic quantum electrodynamics explaining some puzzles that emerge in classical electrodynamics. A chapter is devoted to the study of angular momentum in quantum mechanics, uniquely showing its importance in the understanding of the interaction between the field and charges. The geometry of the space in which the electromagnetic field is embedded is shown to be significant. General relativity provides a relationship between the geometry of space and the presence of matter. The final chapter is devoted to deriving the fundamental equations of general relativity. Mathematical expressions are derived for the effect of gravity on the electromagnetic field, and measurable results are calculated.

The prerequisites of this book are Newtonian physics, calculus and linear algebra. Exercises are provided throughout the book.

Contents:

• The Study of Empty Space
• Fields Produced by Stationary Charges
• Electric Fields and Potentials
• Magnetostatics
• Fields Produced by Time Varying Sources
• Energy and Momentum of Fields
• Special Relativity and Electromagnetism
• Microscopy of the Electromagnetic Field
• The Quantum Mechanics of the Field
• Quantum Angular Momentum and the Field
• Relativistic Quantum Electrodynamics
• Gravity and Electromagnetism

Readership: Advanced undergraduate or graduate students of physics as well as chemists, mathematicians and engineers interested in accessible but rigorous introduction to advanced concepts in electromagnetism.
Key Features:

• An electrodynamics course is an essential part of any graduate or upper level undergraduate physics program. This book meets that need and offers more. It provides a lucid but rigorous and conceptually based introduction to special relativity, quantum mechanics, and general relativity, and explains the relevance of these subjects for electrodynamics. The topics are arranged logically with each chapter building on the preceding material
• The quantum theory of the electromagnetic field is developed conceptually. The need for a quantum theory is demonstrated through an application of the Doppler effect and special relativity. Planck's hypothesis is then applied to the statistical mechanics of blackbody radiation and the quantum formula is obtained. These results are shown to agree with the photoelectric effect and the Compton effect. The interpretation of the quantum theory is offered through the double slit experiment. Quantum field theory follows logically from these early experiments, and the mathematical formalism of quantum mechanics is developed in a simple, logical manner. The physical meaning of the wave function is explained in terms of the field theory. The spins of the photon and the electron are studied quantum mechanically. The solution of Dirac's equation provides an answer to a puzzle that is found in classical electrodynamics
• The derivation of the quantum theory of radiation using the relativistic Doppler formula is just one example of the numerous original approaches followed in this book. Alternative mathematical steps are provided that greatly reduce the tedium of the derivations found in standard textbooks, such as obtaining expressions for the elect

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