Classical electrodynamics : lecture notes
Mechanics
IOP Publishing
2018
EISBN 9780750314046
1. Electric charge interaction.
1.1. The Coulomb law.
1.2. The Gauss law.
1.3. Scalar potential and electric field energy.
1.4. Problems
2. Charges and conductors.
2.1. Polarization and screening.
2.2. Capacitance.
2.3. The simplest boundary problems.
2.4. Using other orthogonal coordinates.
2.5. Variable separation--Cartesian coordinates.
2.6. Variable separation--polar coordinates.
2.7. Variable separation--cylindrical coordinates.
2.8. Variable separation--spherical coordinates.
2.9. Charge images.
2.10. Green's functions.
2.11. Numerical methods.
2.12. Problems
3. Dipoles and dielectrics.
3.1. Electric dipole.
3.2. Dipole media.
3.3. Polarization of dielectrics.
3.4. Electrostatics of linear dielectrics.
3.5. Energy of electric field in a dielectric.
3.6. Problems
4. DC currents.
4.1. Continuity equation and the Kirchhoff laws.
4.2. The Ohm law.
4.3. Boundary problems.
4.4. Energy dissipation.
4.5. Problems
5. Magnetism.
5.1. Magnetic interaction of currents.
5.2. Vector-potential and the Ampère law.
5.3. Magnetic energy, flux, and inductance.
5.4. Magnetic dipole moment, and magnetic dipole media.
5.5. Magnetic materials.
5.6. Systems with magnetics.
5.7. Problems
6. Electromagnetism.
6.1. Electromagnetic induction.
6.2. Magnetic energy revisited.
6.3. Quasi-static approximation and skin effect.
6.4. Electrodynamics of superconductivity and gauge invariance.
6.5. Electrodynamics of macroscopic quantum phenomena.
6.6. Inductors, transformers, and ac Kirchhoff laws.
6.7. Displacement currents.
6.8. Finally, the full Maxwell equation system.
6.9. Problems
7. Electromagnetic wave propagation.
7.1. Plane waves.
7.2. Attenuation and dispersion.
7.3. Reflection.
7.4. Refraction.
7.5. Transmission lines : TEM waves.
7.6. Waveguides : H and E waves.
7.7. Dielectric waveguides, optical fibers, and paraxial beams.
7.8. Resonators.
7.9. Energy loss effects.
7.10. Problems
8. Radiation, scattering, interference, and diffraction.
8.1. Retarded potentials.
8.2. Electric dipole radiation.
8.3. Wave scattering.
8.4. Interference and diffraction.
8.5. The Huygens principle.
8.6. Fresnel and Fraunhofer diffraction patterns.
8.7. Geometrical optics placeholder.
8.8. Fraunhofer diffraction from more complex scatterers.
8.9. Magnetic dipole and electric quadrupole radiation.
8.10. Problems
9. Special relativity.
9.1. Einstein postulates and the Lorentz transform.
9.2. Relativistic kinematic effects.
9.3. Four-vectors, momentum, mass, and energy.
9.4. More on four-vectors and four-tensors.
9.5. Maxwell equations in the four-form.
9.6. Relativistic particles in electric and magnetic fields.
9.7. Analytical mechanics of charged particles.
9.8. Analytical mechanics of the electromagnetic field
10. Radiation by relativistic charges.
10.1. Liénard-Wiechert potentials.
10.2. Radiation power.
10.3. Synchrotron radiation.
10.4. Bremsstrahlung and Coulomb losses.
10.5. Density effects and Cherenkov radiation.
10.6. Radiation's back-action.
10.7. Problems
Appendices. A. Selected mathematical formulas.
B. Selected physical constants.
Essential Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Electrodynamics: Lecture notes is intended to be the basis for a two-semester graduate-level course on electricity and magnetism, including not only the interaction and dynamics charged point particles, but also properties of dielectric, conducting, and magnetic media. The course also covers special relativity, including its kinematics and particle-dynamics aspects, and electromagnetic radiation by relativistic particles.
1.1. The Coulomb law.
1.2. The Gauss law.
1.3. Scalar potential and electric field energy.
1.4. Problems
2. Charges and conductors.
2.1. Polarization and screening.
2.2. Capacitance.
2.3. The simplest boundary problems.
2.4. Using other orthogonal coordinates.
2.5. Variable separation--Cartesian coordinates.
2.6. Variable separation--polar coordinates.
2.7. Variable separation--cylindrical coordinates.
2.8. Variable separation--spherical coordinates.
2.9. Charge images.
2.10. Green's functions.
2.11. Numerical methods.
2.12. Problems
3. Dipoles and dielectrics.
3.1. Electric dipole.
3.2. Dipole media.
3.3. Polarization of dielectrics.
3.4. Electrostatics of linear dielectrics.
3.5. Energy of electric field in a dielectric.
3.6. Problems
4. DC currents.
4.1. Continuity equation and the Kirchhoff laws.
4.2. The Ohm law.
4.3. Boundary problems.
4.4. Energy dissipation.
4.5. Problems
5. Magnetism.
5.1. Magnetic interaction of currents.
5.2. Vector-potential and the Ampère law.
5.3. Magnetic energy, flux, and inductance.
5.4. Magnetic dipole moment, and magnetic dipole media.
5.5. Magnetic materials.
5.6. Systems with magnetics.
5.7. Problems
6. Electromagnetism.
6.1. Electromagnetic induction.
6.2. Magnetic energy revisited.
6.3. Quasi-static approximation and skin effect.
6.4. Electrodynamics of superconductivity and gauge invariance.
6.5. Electrodynamics of macroscopic quantum phenomena.
6.6. Inductors, transformers, and ac Kirchhoff laws.
6.7. Displacement currents.
6.8. Finally, the full Maxwell equation system.
6.9. Problems
7. Electromagnetic wave propagation.
7.1. Plane waves.
7.2. Attenuation and dispersion.
7.3. Reflection.
7.4. Refraction.
7.5. Transmission lines : TEM waves.
7.6. Waveguides : H and E waves.
7.7. Dielectric waveguides, optical fibers, and paraxial beams.
7.8. Resonators.
7.9. Energy loss effects.
7.10. Problems
8. Radiation, scattering, interference, and diffraction.
8.1. Retarded potentials.
8.2. Electric dipole radiation.
8.3. Wave scattering.
8.4. Interference and diffraction.
8.5. The Huygens principle.
8.6. Fresnel and Fraunhofer diffraction patterns.
8.7. Geometrical optics placeholder.
8.8. Fraunhofer diffraction from more complex scatterers.
8.9. Magnetic dipole and electric quadrupole radiation.
8.10. Problems
9. Special relativity.
9.1. Einstein postulates and the Lorentz transform.
9.2. Relativistic kinematic effects.
9.3. Four-vectors, momentum, mass, and energy.
9.4. More on four-vectors and four-tensors.
9.5. Maxwell equations in the four-form.
9.6. Relativistic particles in electric and magnetic fields.
9.7. Analytical mechanics of charged particles.
9.8. Analytical mechanics of the electromagnetic field
10. Radiation by relativistic charges.
10.1. Liénard-Wiechert potentials.
10.2. Radiation power.
10.3. Synchrotron radiation.
10.4. Bremsstrahlung and Coulomb losses.
10.5. Density effects and Cherenkov radiation.
10.6. Radiation's back-action.
10.7. Problems
Appendices. A. Selected mathematical formulas.
B. Selected physical constants.
Essential Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Electrodynamics: Lecture notes is intended to be the basis for a two-semester graduate-level course on electricity and magnetism, including not only the interaction and dynamics charged point particles, but also properties of dielectric, conducting, and magnetic media. The course also covers special relativity, including its kinematics and particle-dynamics aspects, and electromagnetic radiation by relativistic particles.
