If you have additional exercises that would be appropriate for Modern Problems in Classical Electrodynamics, and would be willing to share them, e-mail them to me at the address below. I will be more than pleased to post them on this web site and give you credit for submitting them. Solutions would be useful, too! (I won't post the solutions.)
A large collection of interesting exercises in classical electrodynamics has been posted on the web by Kirk MacDonald, along with links to still more sites.
0. Prologue
0.1. Introduction
0.2. Electrostatics
0.2.1. Charges
0.2.2. Forces and Electric Fields
0.3. Magnetostatics
0.3.1. Currents
0.3.2. Forces and Fields
0.3.3. Vector Potential
0.4. Electrodynamics
0.4.1. Conservation of Charge
0.4.2. Faraday's Law
0.4.3. Energy in the Magnetic Field
0.5. The Maxwell Equations and Electromagnetic Waves
0.5.1. The Maxwell-Ampere Law
0.5.2. Electromagnetic Waves
0.5.3. Potentials and Gauges
0.6. Conservation Laws
0.6.1. Poynting's Theorem
0.6.2. Conservation of Momentum
1. Relativistic Kinematics
1.1. The Principles of Special Relativity
1.1.1. Historical Overview
1.1.2. Einstein's Postulates
1.1.4. Proper Time
1.2. The Lorentz Transformation
1.2.1. Rotation in 4-Space
1.2.2. Time Dilation and Length Contraction
1.2.3. Velocity Transformation
1.3. 4-Vectors and 4-Tensors
1.3.1. Cartesian Tensors
1.3.2. Relativistic Metric and Lorentz Transformation
1.3.3. 4-Vector Calculus
1.4. Electromagnetic Fields
1.4.1. The 4-Tensor Electromagnetic Field
1.4.2. Transformation of Electromagnetic Fields
2. Relativistic Mechanics and Field Theory
2.1. Relativistic Free Particle
2.1.1. Hamilton's Principle and the Calculus of Variations
2.1.2. Langrangian for a Free Particle
2.1.5. Rotational Invariance and Angular Momentum
2.2. Charged Particle in a Vector Potential
2.2.1. Langrangian Mechanics
2.2.3. Canonical Equations of Motion
2.3. The Maxwell Equations
2.3.1. Equations of Motion of a Vector Field
2.4. Invariance and Conservation Laws
2.4.2. Symmetric Stress Tensor for the Electromagnetic Field
3. Time-Independent Electromagnetic Fields
3.1. Electrostatics
3.1.1. Coulomb's Law
3.1.2. Energy in Electrostatic Fields
3.1.3. Multipole Moments
3.2. Boundary-Value Problems with Conductors
3.2.1. Boundary Conditions and Uniqueness Theorems
3.2.2. Energy and Capacitance
3.2.4. Separation of Variables
3.2.5. Spheroidal Coordinates
3.2.6. Spherical Harmonics
3.2.7. Variational Methods
3.2.8. Numerical Methods
3.2.9. Green Functions
3.3. Magnetostatics
3.3.1. Biot-Savart Law
3.3.2. Forces and Energy
3.3.3. Multipole Moments
3.3.4. Magnetic Scalar Potential
4. Electromagnetic Waves
4.1. Plane Waves
4.1.1. Electric and Magnetic Fields in Plane Waves
4.1.2. Charged Particle in a Plane Wave
4.2. Canonical Equations of an Electromagnetic Field
4.2.1. Fourier Decomposition of the Field
4.2.2. Spontaneous Emission by a Harmonic Oscillator
4.2.3. Canonical Equations of the Electromagnetic Field
4.2.4. Blackbody Radiation and the Einstein Coefficients
4.3. Waves in Plasmas
4.3.1. Transverse Electromagnetic Waves
4.3.2. Longitudinal Electrostatic Waves
5. Fourier Techniques and Virtual Quanta
5.1. Fourier Transformation
5.1.1. Fourier's Theorem
5.1.2. Asymptotic Behavior of Fourier Transforms
5.1.3. Delta-Functions
5.1.4. Autocorrelation Functions and the Wiener-Khintchine Theorem
5.1.5. Pulse Compression
5.2. Method of Virtual Quanta
5.2.1. Fourier Decomposition of the Field of a Relativistic Charge
5.2.2. Bremsstrahlung
5.2.3. Excitation by a Fast Charged Particle
5.2.4. Transition Radiation
6. Macroscopic Materials
6.1. Polarization and Magnetization
6.1.1. The Macroscopic Form of the Maxwell Equations
6.1.2. The Constitutive Relations
6.1.3. Boundary Conditions
6.1.4. Magnetic Scalar Potential
6.2. Properties of Dielectric and Magnetic Materials
6.2.1. Dielectric Materials
6.2.2. Magnetic Materials
7. Linear, Dispersive Media
7.1. Linear Media
7.1.1. Waves in a Nondispersive Medium
7.1.2. Constitutive Relations in Dispersive Media
7.1.3. Kramers-Kronig Relations
7.1.4. Plane Waves in Dispersive Media
7.1.5. Phase Velocity and Group Velocity
7.1.6. Conservation of Energy in Dispersive Media
7.2. Reflection and Refraction at Surfaces
7.2.1. Boundary Conditions
7.2.2. Dielectric Reflection
7.2.3. Metallic Reflection
7.3. Energy Loss by Fast Particles Traveling Through Matter
7.3.1. Ionization and Excitation
7.3.2. Relativistic Limit and the Density Effect
8. Nonlinear Optics
8.1. Nonlinear Susceptibility
8.1.1. Nonlinear Polarization
8.1.2. Anisotropic Materials
8.2. Multiphoton Processes
8.2.1. Coupled-Wave Equation
8.2.2. Second-Harmonic Generation
8.2.3. Sum-Frequency Generation
8.3. Nonlinear Index of Refraction
8.3.1. Third-Order Susceptibility
8.3.2. Wave Equation with a Nonlinear Index of Refraction
8.3.3. Phase-Conjugate Reflection
8.4. Raman Processes
8.4.1. Raman Scattering
8.4.2. Coherent Raman Amplification
9. Diffraction
9.1. Geometrical Optics
9.1.1. Eikonal Approximation
9.1.2. Rays in Geometrical Optics
9.1.3. Integral Theorems
9.2. Gaussian Optics and Laser Resonators
9.2.2. Laser Resonators and Mode Spacing
9.3. Diffraction
9.3.1. Scalar Diffraction Theory
9.3.2. Fraunhofer Diffraction (Far Field)
9.3.3. Fresnel Diffraction (Near Field)
10. Radiation by Relativistic Particles
10.1. Angular and Spectral Distribution of Radiation
10.1.1. Fourier Decomposition of the Fields
10.1.2. Retarded Fields and Lienard-Wiechert Fields
10.1.3. Multipole Radiation
10.1.4. Spectral Distribution of Radiation from a Point Charge
10.1.5. Angular Distribution of Radiation from a Point Charge
10.1.6. Total Power Radiated by a Point Charge
10.2. Bremsstrahlung and Transition Radiation
10.2.1. Bremsstrahlung
10.3. Thomson Scattering
10.3.1. Linear Thomson Scattering
10.4. Synchrotron Radiation and Undulator Radiation
10.4.1. Synchrotron Radiation
10.4.2. Undulator Radiation
10.5. Coherent Emission from Multiple Particles
10.5.1. Coherence and Form Factor
10.5.2. Coherent Radiative Processes
10.6. Radiation from Relativistic Particles Traveling Through Matter
10.6.1. Angular Spectral Fluence
10.6.2. Cherenkov Radiation
11. Fundamental Particles in Classical Electrodynamics
11.1. Electromagnetic Mass and the Radiation Reaction
11.1.1. Difficulties in the Classical Theory
11.1.2. The 4/3 Problem and Poincaré Stresses
11.1.3. Point Particles and the Radiation Reaction
11.1.4. Extended Particles
11.2. Magnetic Monopoles
11.2.2. Magnetic Monopoles and Charge Quantization
11.3. Spin
11.3.1. Relativistic Equations of Motion
11.3.2. Thomas Precession and Spin-Orbit Coupling
For information on this web page, contact charles.a.brau@vanderbilt.edu.
Last updated on 6/19/06.