2019 Electromagnetism II

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Academic unit or major
Murakami Syuichi 
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Mode of instruction
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Tue5-6(H116)  Fri5-6(H116)  
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Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Lectures and exercise problems during the course.

Course schedule/Required learning

  Course schedule Required learning
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, Helmhoholtz 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

Reference books, course materials, etc.

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

Assessment criteria and methods

Students will be assesed on their understanding of basis ideas and applications in electrodynamics. The scores are based on excercise problems and final exams.

Related courses

  • ZUB.E202 : Electromagnetism I
  • ZUB.E312 : Electromagnetism III

Prerequisites (i.e., required knowledge, skills, courses, etc.)

non required

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