Principle of Physics IV - Electrodynamics - NSCI004

• Title: Principle of Physics IV - Electrodynamics
• Guaranteed by: Institute of Theoretical Physics (32-UTF)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2022
• Semester: summer
• E-Credits: 5
• Hours per week, examination: summer s.:2/2, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: doc. Mgr. Ondřej Pejcha, Ph.D.

Annotation

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.02.2022)

The course Principles of Physics IV - Electrodynamics will cover advanced concepts of mathematical solutions to the equations of physical fields with principal applications on classical electromagnetism (Maxwell equations) and special relativity both in static and time-dependent situations.

Aim of the course

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.02.2022)

The course Principles of Physics IV - Electrodynamics will cover advanced concepts of mathematical solutions to the equations of physical fields with principal applications on classical electromagnetism (Maxwell equations) and special relativity both in static and time-dependent situations.

The course extends previously introduced concepts with more rigorous treatment of the mathematical formulation, differential operators, orthogonal coordinate systems, series representation of field solutions, and introduction to the theory of distributions. Time-dependent aspects of electromagnetism will be illustrated on moving charges, waves, and conservation laws. Relativistic formulation of electromagnetism will motivate introduction to tensor algebra and basic relativistic effects. Connection with quantum mechanics and related applications will be established.

Course completion requirements

Last update: doc. RNDr. Karel Houfek, Ph.D. (14.05.2023)

The final mark is based on the oral examination (67%) and the results of tests taken during the course (33%). The oral examination takes place during the examination period and students must first obtain the credit for exercises. Credit for exercises is based on the solution of take-home problems (34%) and two tests (midterm and final, each 33%).

Literature

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.02.2022)

1. A. Zangwille, Modern Electrodynamics, Cambridge University Press, 2013

2. D. J. Griffiths, Introduction to Electrodynamics, Cambridge University Press, 2017

3. R. K. Wangsness, Electromagnetic fields, Wiley, 1986

4. J. D. Jackson, Classical Electrodynamics, Wiley, 2012

Requirements to the exam

Last update: doc. RNDr. Karel Houfek, Ph.D. (14.05.2023)

The requirements for the exam correspond to the course syllabus to the extent that was given in the lectures.

Syllabus

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.02.2022)

1. Maxwell equations and electromagnetic potentials. Mathematical formalism (Euclidean space, orthogonal coordinates, 1st and 2nd order vector operators)

2. Green function, introduction to the theory of distributions

3. Multipole expansion, separation of variables, eigenfunction expansion (spherical harmonics)

4. Electrostatics, electric potential, linear and surface charge densities, symmetries, solution in curvilinear coordinates, far-field limit, energy

5. Magnetostatics (magnetic dipole, Lorentz force, quasistationary approximation)

6. Electrodynamics (initial value problem, gauge fixing, moving charge)

7. Waves (plane wave, longitudinal and transverse waves, resonance, dipole radiation, applications to optics)

8. Conservation laws (energy, momentum, angular momentum)

9. Introduction to special relativity

10. Relativistic formulation of electromagnetism

11. Connection between macroscopic and microscopic quantities, linear and non-linear effects