This book summarizes the basics of electricity and magnetism prior to covariant formulation of Maxwell's equations. The book works out the basics of special relativity and then applies the covariant formalism to understand radiation, both in vacuum and in material medium. The emphasis is on cleaner mathematical formalism based on experimental facts. The book contains many problems/exercises which will help the students to understand the basics of the subject. The difference between the present book with existing books of this level lies in the presentation of the topics and the subjects chosen. Instead of resenting a lot of material related to electromagnetism, it presents some very important but selected problems of advanced electromagnetism to students who are learning it for the first time. This book is aimed at graduate/advanced graduate students who have done at least one basic level course in electricity and magnetism.

Autorentext

Dr. Kaushik Bhattacharya obtained his doctoral degree at the Saha Institute of Nuclear Physics, Kolkata. Subsequently he carried out postdoctoral research in Physical Research Laboratory (PRL), Ahmedabad and Instituto de Ciencias Nucleares (ICN) in the National Autononomous University of Mexico (UNAM) in Mexico City. He is a theoretical physicist, whose chief interest lies in cosmology and quantum field theory in curved spacetime. His interests also lie in problems related with astro-particle physics and modified theories of gravity. Dr. Soumik Mukhopadhyay received his doctoral degree from Saha Institute of Nuclear Physics, Kolkata. Later on, he was in the Department of Physics, Indian Institute of Science, Bangalore as a Centenary Postdoctoral Fellow. He is an experimental physicist with research interests in the area of magnetism and strongly correlated electron systems.

Zusammenfassung

This book summarizes the basics of electricity and magnetism prior to covariant formulation of Maxwell's equations. The book works out the basics of special relativity and then applies the covariant formalism to understand radiation, both in vacuum and in material medium. The emphasis is on cleaner mathematical formalism based on experimental facts. The book contains many problems/exercises which will help the students to understand the basics of the subject. The difference between the present book with existing books of this level lies in the presentation of the topics and the subjects chosen. Instead of presenting a lot of material related to electromagnetism, it presents some very important but selected problems of advanced electromagnetism to students who are learning it for the first time. This book is aimed at graduate/advanced graduate students who have done at least one basic level course in electricity and magnetism.

Inhalt

1. Chapter One: Concise summary of basic electrodynamics (a) The emperical laws, Gauss, Biot-Savart, Faraday's law and Lorentz force law (b) Dielectric medium, Magnetic medium (c) Maxwell's equation (d) Macroscopic electrodynamics (e) Poyntings theorem, Maxwell's strss tensor and conservation of energy and momentum (f) Electromagnetic wave propagation in vacuum, concept of polarization, the various polarizations (g) Propagation in medium, dielctric polarization (h) Causality and Kramer's - Kronig relations, examples (i) Spreading of wave-packets (j) Motivation for advanced electrodynamics in covariant formalism. 2. Chapter two: Special Relativity and Fourier transform theory for electrodynamics (a) Postulates of relativity, Lorentz transformations (b) 4-vectors in general, 4-velocities and 4-fources, tensor nature of the quantities, examples of first rank and second rank tensors (c) Fourier analysis, Dirac-Delta function, Folding theorem, Parseval Theorem 3. Chapter three: Maxwell's Equations in absence of material medium (a) Introduction of the 4-vectors Aµ, Jµ and the second rank tensor Fµ. (b) Writing the Maxwell's equation in the covariant form, writing the Lorentz Force equation in covariant form (c) Change of Fµ under a Lorentz transformation, and transformation of electric and magnetic fields, examples by a point charge 4. Chapter four: Gauge symmetry (a) Introduction to gauge transformation. (b) Lorenz gauge condition and Coulomb gauge condition. (c) Examples of various cases where this gauges are used. 5. Chapter five: Electromagnetic field due to a uniformly moving charged particle and uniform linear charge distribution (a) Lorentz transformation of field strength tensor (b) Calculation of the fields due to uniform motion of charge. (c) Caluclation of field due to linear, uniform charge distribution. 6. Chapter six: Action principle in electrodynamics (a) The action principle for continuous fields (b) The discrit symmetries in electrodynamics (c) The form of the Lagrangian in elctrodynamics (d) Euler-Lagrange equation (e) Basics of Hamiltonian formalism, constrained systems 7. Chapter seven: Symmetries and conservation laws (a) Symmetry transformations. (b) Conservation conditions and Noether's theorem (c) Energy-momentum conservation and connection with Pyontings theorem, conservation of enrgy-momentum in presence of charged particles. 8. Chapter eight: Solutions of Maxwell's equations leading to radiation (a) Wave equations in terms of the gauge fields (b) Green's function of the inhomogeneous functions (c) Advanced and retarded potential solutions (d) Dipole radiation (e) Lienard-Weichart Potentials (f) Larmor formula, covariance of Larmor formula (g) Angular distribution of radiation and frequency distribution (h) Radiation reaction, Abraham-Lorentz force 9. Chapter nine: Electrodynamics inside material medium (a) Maxwell's equation in a dispersive medium (b) Scattering phenomena, Rayleigh scattaering, Thomson scattering (c) Causality and Kramer's - Kronig relations, examples 10. Chapter ten: High velocity charged particles inside matrial medium (a) Fields produced by high velocity charged particle inside a dielectric medium (b) Energy loss formula, Cherenkov radiation, its application