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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.
Poslední úprava: Houfek Karel, doc. RNDr., Ph.D. (11.02.2022)
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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. Poslední úprava: Houfek Karel, doc. RNDr., Ph.D. (11.02.2022)
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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%). Poslední úprava: Houfek Karel, doc. RNDr., Ph.D. (14.05.2023)
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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 Poslední úprava: Houfek Karel, doc. RNDr., Ph.D. (11.02.2022)
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The requirements for the exam correspond to the course syllabus to the extent that was given in the lectures. Poslední úprava: Houfek Karel, doc. RNDr., Ph.D. (14.05.2023)
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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, applications to optics) 8. Conservation laws (energy, momentum, angular momentum) 9. Introduction to special relativity 10. Relativistic formulation of electromagnetism Poslední úprava: Pejcha Ondřej, doc. Mgr., Ph.D. (26.01.2026)
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1) Apply advanced vector calculus and coordinate systems to formulate Maxwell’s equations and analyze electromagnetic potentials. 2) Analyze electrostatic and magnetostatic systems using symmetry, Green’s functions, and multipole expansions to solve boundary-value problems. 3) Evaluate electromagnetic fields and potentials generated by static and moving charges, including near- and far-field behavior. 4) Analyze time-dependent electromagnetic phenomena, including wave propagation. 5) Apply conservation laws of energy, momentum, and angular momentum to electromagnetic systems. 6) Explain the principles of special relativity and analyze their implications for classical electromagnetism. Poslední úprava: Pejcha Ondřej, doc. Mgr., Ph.D. (26.01.2026)
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