Advanced electromagnetic theory
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Bibliographic Information
Advanced electromagnetic theory
（Lecture notes in physics, 1009）
Springer Nature Singapore, 2022
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Includes bibliographical references and index
Description and Table of Contents
Description
This textbook provides a comprehensive one-semester course on advanced electromagnetic theory written from the modern perspective covering all important topics that a professional physicist needs to know. Starting from Maxwell's equations, electrostatics and magnetostatics, this book goes on to discuss such topics as relativistic electrodynamics, emission of electromagnetic radiation and plasma physics. It contains solved examples and exercises for students to highlight the concepts in each chapter.
Table of Contents
Chapter 1. Introduction
Lecture 1 - Possibility of axiomatic formulation of electromagnetic Theory.
Basic equations, separation into electrostatics and magnetostatics in the absence
of time dependence. Solution of the general static equations, -function.
Chapter 2. Electrostatics
Lecture 2 - Electrostatic equations, electrostatic potential, Coulomb's law,
Poisson's equation. Potential and electric field due to a dipole and a uniform
dipole surface. Gauss's theorem and applications.
Lecture 3 - Curvilinear coordiates, the Laplacian in cylindrical and spherical
coordinates. Uniqueness theorem for Laplace's equation. Method of images,
point charge in front of plane surface and sphere.
Lecture 4 - Boundary value problems in two-dimensional Cartesian and
polar geometry, general solutions and specific examples.
Lecture 5 - Boundary value problems in axisymmetric spherical geometry,
Legendre polynomials. Multipole expansion for an axisymmetric distribution of
charges.
Lecture 6-Dielectric medium: electric polarization, basic equations, boundary
conditions. Dielectric sphere in uniform electric field. Energy density of
electrostatic fields.
Chapter 3. Magnetostatics
Lecture 7 - Basic equations, vector potential, Biot-Savart law, Ampere's law.
Techniques for solving magnetostatic problems. Magnetic field due to localized
currents.
Lecture 8 - Multipole expansion of magnetostatic fields, magnetic moment.
Magnetic medium, ferromagnetism, example of uniformly magnetized sphere.
Chapter 4. Electrodynamics and Electromagnetic
Waves
Lecture 9 - Maxwell's equations, charge conservation, significance of Faraday's
law of electomagnetic induction. Energy and momentum of electromagnetic
fields, electromagnetic field tensor.
Lecture 10 - Electromagnetic waves in non-conducting medium, polarization,
Stokes parameters. Electromagnetic waves in conducting medium, skin
depth.
Lecture 11 - Reflection and refraction at an interface between two media,
Fresnel formulae, Brewster's law, total internal reflection.
Lecture 12 - Rectangular wave guides, interior equations and boundary
conditions, TE and TM modes. Rectangular cavity resonator.
Chapter 5. Relativity and Electrodynamics
Lecture 13 - Lorentz transformation, transformation of velocities, aberration
of light. Introduction to tensors. Special relativity in 4-vector notation, Doppler
effect.
Lecture 14 - Relativistic mechanics, velocity 4-vector and 4-momentum.
Covariant formulation of electrodynamics, 4-potential, electromagnetic field tensor,
Maxwell's equations in covariant notation.
Lecture 15 - Transformation of electromagnetic fields, Lorentz 4-force. Action
of charged particle in electromagnetic field, Lagrangian formulation of electrodynamics.
Chapter 6. Electrodynamics of Moving Charges
Lecture 16 - Gauge freedom, Lorentz gauge, inhomogeneous wave equation.
Solution of inhomogeneous equations by Green's function.
Lecture 17 - Retarded potential, Lienard-Wiechert potential. Calculation
of the electromagnetic field due to a moving charge.
Lecture 18- Electromagnetic radiation emitted by accelerated charges, Larmor's
formula. Radiation from oscillating currents, centre-fed linear antenna.
Dipole approximation in radiation emission.
Lecture 19 - Radiation from oscillating dipole. Thomson scattering due to
free electrons. Radiation reaction.
Lecture 20 - Harmonically bound electrons and Rayleigh scattering. Relativistic
beaming and synchrotron radiation. Bremsstrahlung.
Chapter 7. Plasma Physics
Lecture 21 - Different approaches to plasma physics. Debye shielding and
quasi-neutrality. Electromagnetic oscillations in cold plasmas, plasma frequency,
propagation of electromagnetic waves.
Lecture 22 - The MHD approximation, basic equations of MHD, induction
equation. Significance of magnetic Reynolds number, theorem of flux freezing,
applications to astrophysics.
Lecture 23 - Plasma confinement with magnetic fields in cylindrical geometry,
qualitative introduction to plasma instabilities. MHD waves in uniformly
magnetized plasma.
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