Starting with vector calculus, this Electricity and Magnetism I course focuses on equations related to electrostatic fields and their solutions. Electromagnetism is the basis for all fields related to electricity, such as circuits, devices, communications, and electrical power. This means electromagnetism is the basis for applications over a wide range in today's industries and daily life. This course facilitates students' understanding of formulas using vector calculus and the equations of electrostatic fields based on them, along with electric field distribution and electric field energy of systems including conductors and dielectric materials. Students will gain the ability to solve unfamiliar cases related to electromagnetism by applying techniques acquired through this course.
By the end of this course, students will be able to:
1) Express the formulas using vector calculus, including the Gauss's theorem.
2) Solve the equation of electrostatic field using the formulas
3) Express the electric field distribution and electric field energy of the system including conductor and dielectric materials.
4) Apply knowledge acquired through this course to solve problems.
vector calculus, ，Gauss's theorem, Strokes' theorem, electrostatic field, Laplace's equation, Poisson's equation, conductor, dielectric material, electric field energy, current
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
At the beginning of each class, solutions to exercise problems assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to what is taught on that day to solve. Before coming to class, students should read the course schedule and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule | Required learning | |
---|---|---|
Class 1 | Scalar product and vector product, line integral | Understand and solve the exercises of scalar product, vector product and line integral. |
Class 2 | Surface integral, solid angle | Understand and solve the exercises of surface integral and solid angle. |
Class 3 | Gradient, divergence, Gauss's theorem | Understand and solve the exercises of gradient, divergence and Gauss's theorem. |
Class 4 | Rotation (Curl), Strokes' theorem | Understand and solve the exercises of rotation (curl) and Strokes' theorem. |
Class 5 | Coulomb's law, electric field distribution, Gauss's law | Understand and solve the exercises of Coulomb's law, electric field distribution and Gauss's law. |
Class 6 | Electric potential distribution | Understand and solve the exercises of electric potential distribution. |
Class 7 | Conductor and electric field, Laplace's equation, Poisson's equation | Understand and solve the exercises of conductor and electric field, Laplace's equation and Poisson's equation. |
Class 8 | Exercise problems to assess the students' level of understanding on what has been taught so far, and explain how to solve the problem. | Review the course contents. Use the exercise problems to better understand the topics covered, and evaluate one’s own progress. |
Class 9 | Solution of electrostatic field (Laplace's equation, Poisson's equation, boundary condition, uniqueness of solutions) | Understand and solve the exercises of electrostatic field (Laplace's and Poisson's equations). |
Class 10 | Solution of electrostatic field (method of images, numerical analysis) | Understand and solve the exercises of method of images, numerical analysis. |
Class 11 | Conductors, potential coefficient, capacity coefficient | Understand and solve the exercises of conductors, potential coefficient and capacity coefficient. |
Class 12 | Capacitance | Understand and solve the exercises of capacitance. |
Class 13 | Dielectric and polarization, electric flux density, basic equations | Understand and solve the exercises of dielectric and polarization, electric flux density and basic equations. |
Class 14 | Electric field energy and forces, principle of virtual work | Understand and solve the exercises of electric field energy and forces and principle of virtual work. |
Class 15 | Conductor and current | Understand and solve the exercises of conductor and current. |
Masahiro Asada and Takuichi Hirano, "Electromagnetism", Tokyo: Baifukan; ISBN-13: 978-4563069810. (Japanese)
Yasuharu Suematsu, "Electromagnetism", Tokyo: Kyoritsu-shuppan; ISBN-13: 978-4320084179. (Japanese)
Makoto Katsurai, "Fundamental electromagnetism for science and engineering" Tokyo: Ohmsha; ISBN-13: 978-4274132186. (Japanese)
Students will be assessed on their understanding of the vector calculus, the equations of electrostatic field, the electric field distribution and electric field energy of the system including conductor and dielectric materials, and their ability to apply them to solve problems. Students' course scores are based on midterm and final exams (~80%, Midterm: Final ~ 4:6) and exercise problems during each class (~20%).
No prerequisites are necessary, but enrollment in the related courses is desirable.