FROM MAXWELL’S EQUATIONS TO FREE AND GUIDED ELECTROMAGNETIC WAVES: AN INTRODUCTION FOR FIRST-YEAR UNDERGRADUATES

FROM MAXWELL’S EQUATIONS TO FREE AND GUIDED ELECTROMAGNETIC WAVES: AN INTRODUCTION FOR FIRST-YEAR UNDERGRADUATES

Library of Congress Cataloging-in-Publication Data

Contents

Preface

About the Authors

Chapter 1: Maxwell’s Equations in Differential Form

1.1. Introduction

1.2. Gauss’s Laws in Differential Form

1.2.1. Divergence of the Electric Field

1.2.2. A Compact Differential Form for Gauss’s Law

1.2.3. Gauss’s Law for Magnetism

1.2.4. Example 1: Point Charge

1.2.5. Example 2: Uniformly Charged Sphere

1.3. Ampère-Maxwell’s Law in Differential Form

1.3.1. Circulation and Curl

1.3.2. The Curl and Ampère-Maxwell’s Law

1.3.3. A Compact Differential Form for Ampère-Maxwell’s Law

1.3.4. Example: Magnetic Field of a Current-Carrying Long Straight Wire

1.4. Faraday’s Law in Differential Form

1.5. Some Concluding Remarks

Appendix 1.1: Gauss’s Law in Dielectrics

Appendix 1.2: Ampère-Maxwell’s Law in Magnetic Materials

Historical Note: The Creative Process in Physics. Maxwell and His Equations

Solved Problems

Chapter 2: Electromagnetic Waves in Free Space

2.1. Plane Electromagnetic Waves

2.1.1. Maxwell’s Equations in the Absence of Electric Charges and Currents

2.1.2. Transverse Character of Electromagnetic Waves

2.1.3. Derivation of the Wave Equation

2.1.4. Harmonic Plane Waves

2.2. Energy of Electromagnetic Waves

2.2.1. Energy Density

2.2.2. Energy Flux of an Electromagnetic Wave

2.2.3. Intensity of a Harmonic Electromagnetic Wave

Historical Note: Electromagnetic Theory, Oliver Heaviside and the Invention of Vector Analysis

Solved Problems

Chapter 3: Guided Electromagnetic Waves

3.1. Introduction

3.2. The Parallel-Plate Waveguide: TE Modes

3.2.1. A Boundary Condition for the Electric Field

3.2.2. Electric Field in TE Modes

3.2.3. Dispersion Relation and Cutoff Frequencies

3.2.4. The Magnetic Field and the Poynting Vector

3.2.5. Phase Velocity and Group Velocity

3.3. The Parallel-Plate Waveguide: TM and TEM Modes

3.3.1. A Boundary Condition for the Magnetic Field

3.3.2. Fields and Cutoff Frequencies in TM Modes

3.3.3. TEM Modes

3.4. Rectangular Waveguide: TE Modes

3.4.1. Electric Field

3.4.2. Cutoff Frequencies and Dispersion Relation

3.4.3. Magnetic Field

3.4.4. Transmitted Power

3.5. Rectangular Waveguide. TM Modes

3.5.1. Another Boundary Condition for the Magnetic Field

3.5.2. Deriving the Fields and the Cutoff Frequencies

3.5.3. Do TEM Modes Propagate Along a Rectangular Waveguide?

3.6. Summary

Appendix 3.1: Wave Equation in Several Dimensions

Historical Note: The Beginning of Telecommunications and the Discovery of the Largest Waveguide in the World

Solved Problems

Further Reading