# Classical Electrodynamics: An Indian Adaptation

ISBN: 9789388991070

832 pages

## Description

Classical Electrodynamics is a comprehensive and classical text for an undergraduate course in electricity and magnetism and graduate course in classical electromagnetism for students majoring in physics and related fields. The goal of the text is threefold. First goal is to provide the basic subject matter as a coherent whole, together in their physical and mathematical description mode; second is to develop and utilize the topics in mathematical physics and third is to present the interactions of relativistic charged particles with electromagnetic fields; thus making this book useful for theoretical physics, experimental nuclear and high-energy physics.

Introduction and Survey

I.1 Maxwell Equations in Vacuum, Fields, and Sources

I.2 Inverse Square Law or the Mass of the Photon

I.3 Linear Superposition

I.4 Maxwell Equations in Macroscopic Media

I.5 Boundary Conditions at Interfaces between Different Media

I.6 Some Remarks on Idealizations in Electromagnetism

Chapter 1 / Introduction to Electrostatics

1.1 Coulomb’s Law

1.2 Electric Field

1.3 Gauss’s Law

1.4 Differential Form of Gauss’s Law

1.4 Another Equation of Electrostatics and the Scalar Potential

1.6 Surface Distributions of Charges and Dipoles; Discontinuities in the Electric Field and Potential

1.7 Poisson and Laplace Equations

1.8 Green’s Theorem

1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions

1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function

1.11 Electrostatic Potential Energy and Energy Density; Capacitance

Chapter 2 / Boundary-Value Problems in Electrostatics: I

2.1 Method of Images

2.2 Point Charge in the Presence of a Grounded Conducting Sphere

2.3 Point Charge in the Presence of a Charged, Insulated, Conducting Sphere

2.4 Point Charge Near a Conducting Sphere at Fixed Potential

2.5 Conducting Sphere in a Uniform Electric Field by Method of Images

2.6 Green Function for the Sphere; General Solution for the Potential

2.7 Conducting Sphere with Hemispheres at Different Potentials

2.8 Orthogonal Functions and Expansions

2.9 Separation of Variables; Laplace Equation in Rectangular Coordinates

2.10 A Two-Dimensional Potential Problem; Summation of a Fourier Series

2.11 Fields and Charge Densities in Two-Dimensional Corners and Along Edges

2.12 Introduction to Finite Element Analysis for Electrostatics

Chapter 3 / Boundary-Value Problems in Electrostatics: II

3.1 Laplace Equation in Spherical Coordinates

3.2 Legendre Equation and Legendre Polynomials

3.3 Boundary-Value Problems with Azimuthal Symmetry

3.4 Behavior of Fields in a Conical Hole or Near a Sharp Point

3.5 Associated Legendre Functions and the Spherical Harmonics

3.6 Addition Theorem for Spherical Harmonics

3.7 Laplace Equation in Cylindrical Coordinates; Bessel Functions

3.8 Boundary-Value Problems in Cylindrical Coordinates

3.9 Expansion of Green Functions in Spherical Coordinates

3.10 Solution of Potential Problems with the Spherical Green Function Expansion

Chapter 4 / Multipoles, Electrostatics of Macroscopic Media, Dielectrics

4.1 Multipole Expansion

4.2 Multipole Expansion of the Energy of a Charge Distribution in an External Field

4.3 Elementary Treatment of Electrostatics with Ponderable Media

4.4 Boundary-Value Problems with Dielectrics

4.5 Molecular Polarizability and Electric Susceptibility

4.6 Models for the Molecular Polarizability

4.7 Electrostatic Energy in Dielectric Media

Chapter 5 / Magnetostatics, Faraday’s Law, Quasi-Static Fields

5.1 Introduction and Definitions

5.2 Biot and Savart Law

5.3 Differential Equations of Magnetostatics and Ampère’s Law

5.4 Vector Potential

5.5 Vector Potential and Magnetic Induction for a Circular Current Loop

5.6 Magnetic Fields of a Localized Current Distribution, Magnetic Moment

5.7 Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction

5.8 Macroscopic Equations, Boundary Conditions on B and H

5.9 Methods of Solving Boundary-Value Problems in Magnetostatics

5.10 Uniformly Magnetized Sphere

5.11 Magnetized Sphere in an External Field; Permanent Magnets

5.12 Numerical Methods for Two-Dimensional Magnetic Fields

5.13 Faraday’s Law of Induction

5.14 Energy in the Magnetic Field

5.15 Energy and Self- and Mutual Inductances

5.16 Quasi-Static Magnetic Fields in Conductors; Eddy Currents; Magnetic Diffusion

Chapter 6 / Maxwell Equations, Conservation Laws

6.1 Maxwell’s Displacement Current; Maxwell Equations

6.2 Vector and Scalar Potentials

6.3 Gauge Transformations, Lorenz Gauge, Coulomb Gauge

6.4 Green Functions for the Wave Equation

6.5 Retarded Solutions for the Fields: Jefimenko’s Generalizations of the Coulomb and Biot–Savart Laws; Heaviside– Feynman Expressions for Fields of Point Charge

6.6 Poynting’s Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields

6.7 Transformation Properties of Electromagnetic Fields and Sources Under Rotations, Spatial Reflections, and Time Reversal

6.8 On the Question of Magnetic Monopoles

6.9 Discussion of the Dirac Quantization Condition

6.10 Polarization Potentials (Hertz Vectors)

Chapter 7 / Plane Electromagnetic Waves and Wave Propagation

7.1 Plane Waves in a Nonconducting Medium

7.2 Linear and Circular Polarization; Stokes Parameters

7.3 Reflection and Refraction of Electromagnetic Waves at a Plane Interface between Dielectrics

7.4 Polarization by Reflection and Total Internal Reflection; Goos–Hänchen Effect

7.5 Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas

7.6 Simplified Model of Propagation in the Ionosphere and Magnetosphere

7.7 Magnetohydrodynamic Waves

7.8 Superposition of Waves in One Dimension; Group Velocity

7.9 Illustration of the Spreading of a Pulse as It Propagates in a Dispersive Medium

7.10 Causality in the Connection between D and E; Kramers–Kronig Relations

Chapter 8 / Waveguides, Resonant Cavities, and Optical Fibers

8.1 Fields at the Surface of and Within a Conductor

8.2 Cylindrical Cavities and Waveguides

8.3 Waveguides

8.4 Modes in a Rectangular Waveguide

8.5 Energy Flow and Attenuation in Waveguides

8.6 Resonant Cavities

8.7 Power Losses in a Cavity; Q of a Cavity

8.8 Earth and Ionosphere as a Resonant Cavity: Schumann Resonances

8.9 Multimode Propagation in Optical Fibers

8.10 Modes in Dielectric Waveguides

Chapter 9 / Radiating Systems, Multipole Fields and Radiation

9.1 Fields and Radiation of a Localized Oscillating Source

9.2 Electric Dipole Fields and Radiation

9.3 Magnetic Dipole and Electric Quadrupole Fields

9.4 Center-Fed Linear Antenna

9.5 Spherical Wave Solutions of the Scalar Wave Equation

9.6 Multipole Expansion of the Electromagnetic Fields

9.7 Properties of Multipole Fields; Energy and Angular Momentum of Multipole Radiation

9.8 Angular Distribution of Multipole Radiation

9.9 Sources of Multipole Radiation; Multipole Moments

9.10 Multipole Radiation from a Linear, Center-Fed Antenna

Chapter 10 / Scattering and Diffraction

10.1 Scattering at Long Wavelengths

10.2 Scalar Diffraction Theory

10.3 Vector Equivalents of the Kirchhoff Integral

10.4 Vectorial Diffraction Theory

10.5 Babinet’s Principle of Complementary Screens

10.6 Diffraction by a Circular Aperture; Remarks on Small Apertures

10.7 Scattering in the Short-Wavelength Limit

10.8 Optical Theorem and Related Matters

Chapter 11 / Special Theory of Relativity

11.1 The Situation Before 1900, Einstein’s Two Postulates

11.2 Some Recent Experiments

11.3 Lorentz Transformations and Basic Kinematic Results of Special Relativity

11.4 Addition of Velocities, 4-Velocity

11.5 Relativistic Momentum and Energy of a Particle

11.6 Mathematical Properties of the Space-Time of Special Relativity

11.7 Matrix Representation of Lorentz Transformations, Infinitesimal Generators

11.8 Thomas Precession

11.9 Invariance of Electric Charge; Covariance of Electrodynamics

11.10 Transformation of Electromagnetic Fields

11.11 Note on Notation and Units in Relativistic Kinematics

Chapter 12 / Dynamics of Relativistic Particles and Electromagnetic Fields

12.1 Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields

12.2 Motion in a Uniform, Static Magnetic Field

12.3 Motion in Combined, Uniform, Static Electric and Magnetic Fields

12.4 Particle Drifts in Nonuniform, Static Magnetic Fields

12.5 Lowest Order Relativistic Corrections to the Lagrangian for Interacting Charge Particles: The Darwin Lagrangian

12.6 Lagrangian for the Electromagnetic Field

12.7 Proca Lagrangian; Photon Mass Effects

12.8 Effective “Photon” Mass in Superconductivity; London Penetration Depth

12.9 Canonical and Symmetric Stress Tensors; Conservation Laws

12.10 Solution of the Wave Equation in Covariant Form; Invariant Green Functions

Chapter 13 / Collisions, Energy Loss, and Scattering of Charged Particles;

Cherenkov and Transition Radiation

13.1 Energy Transfer in a Coulomb Collision Between Heavy Incident Particle and

Stationary Free Electron; Energy Loss in Hard Collisions

13.2 Energy Loss from Soft Collisions; Total Energy Loss

13.3 Density Effect in Collisional Energy Loss

13.4 Cherenkov Radiation

13.5 Elastic Scattering of Fast Charged Particles by Atoms

13.6 Transition Radiation

Chapter 14 / Radiation by Moving Charges

14.1 Liénard–Wiechert Potentials and Fields for a Point Charge

14.2 Total Power Radiated by an Accelerated Charge: Larmor’s Formula and Its Relativistic Generalization

14.3 Angular Distribution of Radiation Emitted by an Accelerated Charge

14.4 Frequency Spectrum of Radiation Emitted by a Relativistic Charged Particle in Instantaneously Circular Motion

14.5 Undulators and Wigglers for Synchrotron Light Sources

14.6 Thomson Scattering of Radiation

Chapter 15 / Bremsstrahlung, Radiative Beta Processes

15.1 Radiation Emitted During Collisions

15.2 Bremsstrahlung in Coulomb Collisions

15.3 Screening Effects; Relativistic Radiative Energy Loss

15.4 Radiation Emitted During Beta Decay

Chapter 16 / Radiation Damping, Classical Models of Charged Particles

16.1 Introductory Considerations

16.2 Radiative Reaction Force from Conservation of Energy

16.3 Abraham–Lorentz Evaluation of the Self-Force

16.4 Relativistic Covariance; Stability and Poincaré Stresses

16.5 Covariant Definitions of Electromagnetic Energy and Momentum

16.6 Covariant Stable Charged Particle

16.7 Line Breadth and Level Shift of a Radiating Oscillator

16.8 Scattering and Absorption of Radiation by an Oscillator

A / Appendix on Units and Dimensions

A.1 Units and Dimensions; Basic Units and Derived Units

A.2 Electromagnetic Units and Equations

A.3 Various Systems of Electromagnetic Units

A.4 Conversion of Equations and Amounts Between SI Units and Gaussian Units

B / Appendix on Equations of Macroscopic Electromagnetism

References and Suggested Reading

Index