2025 (Current Year) Faculty Courses School of Science Undergraduate major in Physics
Electromagnetism II (Lecture)
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Fumitaka Kagawa
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- PHY.E212
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Apr 2, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course deals with advanced topics in electromagnetism. Based on the Maxwell equations, I discuss their solution in a 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.
Course description and aims
You will be able to understand the basics and applications of the Maxwell equations through many examples. In particular, an
electromagnetic wave in a 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.
Keywords
Maxwell equation, electromagnetic wave, propagaton, radiation, scattering, theory of special relativity
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Explain basic concepts by use of blackboard.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Maxwell equations, the energy and the momentum of electromagnetic fields, Maxwell stress | Understand Maxwell equations, the energy and the momentum of electromagnetic fields, Maxwell stress |
| Class 2 | propagation of the electromagnetic waves, plane wave solutions of electric magnetic fields, polarization, and Helmholtz equations and boundary conditions | Understand the plane wave solution of the electromagnetic wave in space and its polarization, general propagation, Helmholtz equations, and boundary conditions of fields |
| Class 3 | Waveguide, TE wave, TM wave, TEM wave, phase velocity, and group velocity | Understand the propagation of electromagnetic wave through the waveguide |
| Class 4 | Diffraction of electromagnetic wave, Fresnel‒Kirchhoff'S formula, Fraunhofer diffraction, Fresnel diffraction | Understand the diffraction phenomena of electromagnetic waves from the wave equation |
| Class 5 | Electromagnetic potential and gauge transformation | Understand the Maxwell equation using electromagnetic potentials |
| Class 6 | Coulomb gauge, Lorenz gauge, and Green functions for the Helmholtz equations | Understand the Coulomb gauge, the Lorenz gauge, and the solution of 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, and Lorentz transformation | Understand basic concepts of special relativity |
| Class 9 | relativistic mechanics of particles, contravariant and covariant vectors | Understand relativistic mechanics of particles, contravariant and covariant vectors |
| Class 10 | variational principle and equation for electromagnetic fields | Derive the Maxwell equations from the variational principle |
| Class 11 | Canonical formalism of electromagnetic fields | Understand canonical formalism and conservation laws of electromagnetic fields |
| Class 12 | Radiation from moving charged particles and Lienard‒Wiechert potential | Understand radiation from moving charged particles |
| Class 13 | Bremsstrahlung and Cynclotron radiation | Understand some examples of radiation from a accelerated charged particle |
| Class 14 | scattering of electromagnetic waves by a charged particle | Understand scattering of electromagnetic waves by a charged particle |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content (including assignments) for each class.
They should do so by referring to textbooks and other course materials.
Textbook(s)
Handouts will be distributed in the lectures
Reference books, course materials, etc.
Shigenobu Sunagawa, Theory of Electromangetism, Kinokuniya Shoten (Japanese)
Makoto Oka, Classical Theory of Electromagnetic Fields, Baifukan (Japanese)
Koichi Ota, Foundations of Electrodynamics II, Springer (Japanese)
Landau and Lifshitz, Classical Theory of Fields, Pergamon
J.D. Jackson, Classical Electrodynamics, Wiley
Evaluation methods and criteria
Students will be assessed on their understanding of basis ideas and applications in electrodynamics. The scores are based on the report problems or the final exams.
Related courses
- PHY.E205 ： Electromagnetism
- PHY.Q206 ： Analytical Mechanics(Lecture)
- PHY.E310 ： Electromagnetism III(Lecture)
Prerequisites
None.