COURSE GOALS:
- acquire knowledge and understanding of the theory of Classical electrodynamics (CED)
- acquire operational knowledge from methods used to solve problems in CED
- acquire an overview of the use of CED in modern areas of physics
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
1. KNOWLEDGE AND UNDERSTANDING
1.1 formulate, discuss and explain the basic laws of physics including mechanics, electromagnetism and thermodynamics
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
4. COMMUNICATION SKILLS
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
5.2 remain informed of new developments and methods and provide professional advice on their possible range and applications
5.3 carry out research by undertaking a PhD
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon passing the course on Classical electrodynamics, the student will be able to:
- demonstrate knowledge of vector analysis, concepts of gradient, divergence, curl, Helmholts theorem for vector fields
- formulate electrostatics by using divergence and curl of electric fields, demonstrate knowledge of Gauss law and scalar potential
- demonstrate knowledge of Poisson and Laplace equations, uniqueness theorems for these equations, separation of variables in Cartesian, cylindrical and spherical coordinate systems
- demonstrate knowledge of method of images and multipole expansion
- demonstrate knowledge of electrostatics in the presence of conductors and dielectrics, polarization, dielectric displacement vector, polarizability and susceptibility, macroscopic and microscopic fields
- formulate magnetstatics by using rotation and curl of magnetic fields, demonstrate knowledge of Biot-Savart law, Lorentz force, and vector potential
- demonstrate knowledge of magnetostatics in the presence of magnetic materials, paramagnetism, diamagnetism, auxiliary field H, magnetic susceptibility and permeability
- demonstrate knowledge of Faradey's law of induction, electromotive force, inductivity
- demonstrate knowledge of Maxwell equations, boundary conditions for fields and potentials at the boundary between different media
- demonstrate knowledge of the laws of conservation of energy, momentum and angular momentum in CED, Poynting theorem, Poynting vector, Maxwell tensor
- formulate and interpret CED by using scalar and vector potential, demonstrate knowledge of different gauges, retarded potential, Lienard-Wiechart potential
- demonstrate knowledge of electromagnetic waves in vacuum, systems with dielectrics, reflection and refraction, waveguides and cavities made od conductors and dielectrics
- solve wave equations by using principle of superposition, demonstrate knowledge of wave dispersion
- demonstrate knowledge of the basic model for frequency dependent susceptibility/dielectric response, connection between the real and imaginary part of the dielectric function, dispersion relation for plasma
- demonstrate knowledge of the electric and magnetic dipole radiation, radiation of an arbitrary distribution of charge and radiation of moving point charges
- demonstrate knowledge and understanding of the connection between CED and Special Theory of Relativity, Einstein postulates, geometry of space-time, Lorentz transformations, transformations of electromagnetic fields, tensor formulation of CED
COURSE DESCRIPTION:
Lectures per weeks (30 weeks in total):
The Fall semester
1. week - vector analysis (gradient, divergence, curl)
2.-3. week - electrostatics (Gauss law, scalar potential), electrostatics with conductors, energy in electrostatic fields
4.-5. week - special techniques (separation of variables for Laplace and Poisonn equation, method of images and multipole expansion)
6.-7. week - electrostatics in the presence of dielectrics (atomic polarizability, polarization, field of a polarized object, dielectric displacement, susceptibility, macroscopic and microscopic fields, energy of electrostatic fields in the presence of dielectrics
8.-9. week - magnetostatics (Biot-Savart law, Lorentz force, vector potential);
10.-11. week - magnetostatics in the presence of materials (paramagnetism, diamagnetism, ferromagnetism, auxiliary field H, magnetic permeability and susceptibility
12.-15. week - Faradey's law of induction, electromotive force, inductivity, Maxwell equations, boundary conditions
The Summer semester
16.-17. week - Poynting theorem, Poynting vector, Maxwell tensor
18.-21. week - electromagnetic waves (waves in vacuum, systems with dielectrics, reflection and refraction), model frequency dependent dielectric response, propagation of wave packets, dispersion and group velocity, waveguides (dielectric and with conductors), electromagnetic cavities
22.-24. week - formulation of classical electrodynamics via scalar and vector potential, gauge fields, retarded potentials, Lienard-Wiechart potential, Jefimenko's equations
25.-27. week - electric and magnetic dipole radiation, radiation of an arbitrary distribution of charge and moving point charges
28.-30. week - CED and Special Theory of Relativity, Einstein postulates, Lorentz transformations, transformations of electromagnetic fields, tensor formulation of CED
Exercises follow lectures by content:
The Fall semester
1. week - vector analysis
2.-3. week - electrostatics, electrostatics with conductors
4.-5. week - special techniques (separation of variables for Laplace and Poisonn equation, method of images and multipole expansion)
6.-7. week - electrostatics in the presence of dielectrics
8.-9. week - magnetostatics
10.-11. week - magnetostatics in the presence of materials
12.-15. week - Maxwell equations, boundary conditions, Faradey's law of induction
The Summer semester
16.-17. week - Poynting theorem, Poynting vector, Maxwell tensor
18.-21. week - electromagnetic waves, model frequency dependent dielectric response, propagation of wave packets, dispersion and group velocity, waveguides, electromagnetic cavities
22.-24. week - formulation of classical electrodynamics via scalar and vector potential, gauge fields, retarded potentials, Lienard-Wiechart potential, Jefimenko's equations
25-27. week - electric and magnetic dipole radiation, radiation of an arbitrary distribution of charge and moving point charges
28.-30. week - CED and Special Theory of Relativity, Einstein postulates, Lorentz transformations, transformations of electromagnetic fields, tensor formulation of CED
REQUIREMENTS FOR STUDENTS:
Students must attend 30% of the written exams (quizes and mid-term) before the end of the 2nd semester.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Grading and assessing the work of students during the semesters:
- There are at least four "quiz" written exams (four problems to solve in a quiz)
- There is a mid-term written exam
Grading after the second semester:
- final written and oral exam
Contributions to the final grade:
- one third of the grade are carried by the results of the quiz exams (if the student does not attend the quiz it counts as not sufficient), the worst quiz result does not enter into the final grading (2+2 ECTS points)
- one third of the grade are carried by the results of the mid-term and final written exam (2+2 ECTS points)
- the oral exam carries one third of the grade (2+2 ECTS points).
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