This course deals with advanced topics in electromagnetism. Based on the Maxwell equations, I discuss their solution in vacuum, propagation, radiation and scattering of electromagnetic waves. I also discuss special relativity and manifest Lorentz covariant formulation of electrodynamics. The relativistic motion of a charged particle in an electromagnetic field and radiation from an accelerated charged particle are explained. Physics of electromagnetic fields is a foundation of physics and modern technology. The principle of relativity and fields are important subjects which play an important role in understanding modern physics. The aim of this course is to get basic concepts in electrodynamics and apply them to various problems starting from the Maxwell equations.
You will be able to understand the basics and applications of the Maxwell equations by many examples. Especially an
electromagnetic wave in vacuum, and its propagation, radiation and scattering are mainly focused on. You will also understand how special relativity is important in electrodynamics. You will also be able to understand the motion of a charged particle and radiation from an accelerated source.
Maxwell equation, electromagnetic wave, propagaton, radiation, scattering, theory of special relativity
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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lectures and exercises
Course schedule | Required learning | |
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Class 1 | Maxwell equations, energy and momentum of electric magnetic fields and their conservation laws | Understand energy, momentum of electric mangentic fields and their conservations |
Class 2 | propagation of electromagnetic wave, plane wave solutions of electric magnetic fields, polarization, and Helmholtz equations and boundary conditions | Understand plane wave solution of the electromagnetic wave in space and its polarization, general propagation, Helmholtz equations and boundary conditions of fields |
Class 3 | Wave guide, TE wave, TM wave, TEM wave, phase velocity and group velocity | Understand propagation of electromagnetic wave through the wave guide |
Class 4 | Diffraction of electromagnetic wave, Fresnel‒Kirhihoff'S formula, Fraunhofer difraction, Fresnel diffraction | Understand diffraction phenomena of electromagnetic wave from the wave equation |
Class 5 | Electromegnetic potential and gauge transformation, Coulomb gauge and Lorenz gauge | Understand the Maxwell equation using electromegnetic potentials |
Class 6 | radiation from sources, Green functions for the Helmholtz equations | Understand the radiation of electromagnetic fields by solving the Helmholtz equation via the Green function method |
Class 7 | electric dipole and magnetic dipole radiations | Understand dipole radiations as examples of radiations |
Class 8 | special relativity theory, Lorentz transformation and relativistic mechanics | Understand basic concepts of special relativity |
Class 9 | covariant formulation of electromagnetic fields | Understand manifestly Lorentz covariant form of the Maxwell equations |
Class 10 | relativistic mechanics of charged particle in electromagnetic fields | Understand relativistic mechanics of a relativistic charged particle |
Class 11 | variational principle and equation for electromagnetic fields | Derive the Maxwell equations from the variational principle |
Class 12 | Canonical formalism of electromagnetic fields | Understand canonical formalism and conservation laws of electromagnetic fields |
Class 13 | Radiation from accelerated charged particle and Lienard‒Wiechert potential | Understand radiation from accelerated charged particle |
Class 14 | Bremsstrahlung and Cynclotron radiation | Understand some examples of radiation from a accelerated charged particle |
Class 15 | scattering of electromagnetic waves by a charged particle | Understand scattering of electromagnetic waves by a charged particle |
none specified
Makoto Oka, classical theory of electromagnetic fields, Baifukan (Japanese)
Landau and Lifshitz, Classical Theory of Fields, Pergamon
Shigenobu Sunagawa, Theory of Electromangetism, Kinokuniya Shoten (Japanese)
J.D. Jackson, Classical Electrodynamics, Wiley
Students will be assessed on their understanding of basis ideas and applications in electrodynamics. The scores are based on
exercise problems and final exams.
non required