Basic Electromagnetic Theory · Field Theory Foundations and Structure by Babington, James -- Read -- Imperial Library of Trantor

Index

Cover Page Halftitle Title Page Copyright Contents Preface 1 Introduction

1.1 General Remarks

2 Mathematical Topics

2.1 Summary of Necessary Mathematical Formulae

2.1.1 Some Basic Group Theory 2.1.2 Operators and Eigenvalue Business 2.1.3 Differential Vector Calculus 2.1.4 Integral Vector Calculus 2.1.5 Functions, Distributions, and All Things Fourier

2.2 Coordinate Systems and Transformations 2.3 Physical Constants and Useful Numbers

3 Maxwell’s Equations Part I

3.1 The law of Coulomb - Electric Charge, Force, and Basic Measurement 3.2 The law of Gauss - The Electric Field and Some Basic Math 3.3 The “Magnetic” Law or the Law with no Name 3.4 Voltage and Capacitance 3.5 Summary

4 Maxwell’s Equations Part II

4.1 The Conservation of Charge 4.2 Electric Currents and the Law of Ampère

4.3 The Law of Faraday 4.4 The Displacement Current 4.5 Summary

5 Physical Degrees of Freedom

5.1 The Wave Equation and Solutions 5.2 Basic Wave Solutions - Scalar Field Theory

5.2.1 Solutions in Spherical Coordinates 5.2.2 Solutions in Cylindrical Coordinates 5.2.3 Comments

5.3 Degrees of Freedom - Polarization

5.4 Gauge Invariance and Potentials 5.5 Summary

6 Physical Observables

6.1 The RLC Circuit 6.2 Field Energy, Momentum, and Angular Momentum

6.2.1 The Stress Tensor and Conservation of Momentum 6.2.2 The Poynting Vector and Energy Conservation 6.2.3 Conservation of Angular Momentum

6.3 Polarization (Again) Courtesy of Stokes 6.4 Summary

7 Distributions of Charge, Macroscopic Matter, and Boundary Conditions

7.1 Multipoles

7.1.1 Interlude on Electric and Magnetic Dipoles

7.2 Boundary Conditions 7.3 Electromagnetic Interactions with Matter 7.4 Electrical Conductivity 7.5 Field Equations with General Matter 7.6 Summary

8 Conclusions and Omissions Exercises and Solutions Bibliography Index