Maxwell's Equations and Their Consequences

Elementary Electromagnetic Theory Volume 3: Maxwell’s Equations and their Consequences is the third of three volumes that intend to cover electromagnetism and its potential theory. The third volume considers the implications of Maxwell's equations, such as electromagnetic radiation in simple cases, and its relation between Maxwell's equation and the Lorenz transformation. Included in this volume are chapters 11-14, which contain an in-depth discussion of the following topics: • Electromagnetic Waves • The Lorentz Invariance of Maxwell's Equation • Radiation • Motion of Charged Particles Intended to serve as an introduction to electromagnetism and potential theory, the book is for second, third, and fourth year undergraduates of physics and engineering, as they are included in their course of study. Do note that the authors assume that the readers are conversant with the basic ideas of vector analysis, including vector integral theorems.

Preface to Volume 3

11. Electromagnetic Waves

11.1 Plane Electromagnetic Waves

11.2 Reflection and Transmission: Normal Incidence

11.3 Reflection and Refraction: Oblique Incidence

11.4 Energy Relations for Oblique Incidence

11.5 Total Internal Reflection

11.6 Propagation of Waves in a Conducting Medium

11.7 Waveguides

11.8 The Transmission Line

12. The Lorentz Invariance of Maxwell's Equations

12.1 Groups of Transformations

12.2 Four-Vectors and Six-Vectors

12.3 The Lorentz Group

12.4 Maxwell's Equations

12.5 The Electromagnetic Potentials

13. Radiation

13.1 General Properties of Radiation

13.2 The Hertz Vector

13.3 Solutions with Axial Symmetry

13.4 Discussion of the Field Strength

13.5 Interpretation of the Results

13.6 Other Kinds of Radiative Solutions

13.7 The Fields of Moving Charges

13.8 The Liénard-Wiechert Potentials

13.9 Calculation of the Field Strengths

14. The Motion of Charged Particles

14.1 Introduction

14.2 Non-Relativistic Motion of an Electric Charge in an Electromagnetic Field

14.3 Charged Particles and Currents

14.4 Relativistic Motion of Charges

Answers to the Exercises

Index