UFPF004 Selected Topics in Physics II

Faculty of Philosophy and Science in Opava
Summer 2016
Extent and Intensity
3/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Pavel Bakala, Ph.D. (lecturer)
prof. Ing. Ivan Hubač, DrSc. (lecturer)
RNDr. Pavel Bakala, Ph.D. (seminar tutor)
prof. Ing. Ivan Hubač, DrSc. (seminar tutor)
RNDr. Kateřina Klimovičová, Ph.D. (seminar tutor)
Guaranteed by
prof. Ing. Ivan Hubač, DrSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This semester course introduces selected topics of special theory relativity and classical electrodynamics. Important applications and examples completing the theoretical treatment are illustrated using the symbolic and numerical demonstrations in Mathematica.
Syllabus
  • Inconsistency of Newtonian mechanics and Maxwellian electrodynamics, ether and attempts of its detection. Mach's principle. Postulates of special theory of relativity. Inertial system, Einstein's principle of relativity, the principle of constant speed of light clock synchronization, relativity of simultaneity, time dilation and its experimental evidence, length contraction.
    Lorentz transform, transformation of the components of velocity and acceleration spacetime interval and the light cone, causality infinitesimal Lorentz transform. Examples (graphical treatment of relativistic velocity addition).
    Minkowski spacetime. Geometric interpretation of special Lorentz transform, world lines, world tubes surfaces and hypersurface in spacetime, general Lorentz group and its subgroups. 4-tensors in Minkowski spacetime, the metric tensor, transformation properties of tensors 4-velocity and 4-acceleration. Examples (demonstration of causality by the means of geometrical interpretation of Lorentz transform).
    Maxwell's equations. Conservation laws. Differential and integral form of the general equation of continuity for tensor quantities conservation of electric charge, energy, momentum and angular momentum illustrations. Examples (a demonstration of the general form of the equation of continuity).

    Electrostatic field, Gauss' law of electrostatics, potential, Laplace and Poisson equations, Coulomb's law. Calculation of electrostatic field, electrostatic energy, multipole expansion, dipole and quadrupole moment, system of charges in an external field field lines and equipotentials. Examples (numerical methods for calculating electrostatic fields).
    Magnetic field of a steady current. Problem definition, vector potential, Ampere and Biot-Savart's law, electrostatic-magnetic analogy, multipole expansion, the magnetic dipole moment and the behavior in an external magnetic field, the field lines. Examples (numerical methods of calculation of magnetic fields).
    Time-varying fields. Electromagnetic potentials, calibration transforma and gauge invariance. Homogeneous wave equation, plane electromagnetic wave, its structure and properties. Inhomogeneous wave equation. Advanced and retarded potentials, field of a moving point charge (Liénard-Wiechert potentials). Radiative and nonradiative field, field of a uniform rectilinear motion of a point charge radiation of electromagnetic waves. Examples (structure of a plane wave and the aberration of light).
    Field of an island charge system at a large distance, the wave zone, electric dipole radiation, magnetic dipole radiation, electrical quadrupole radiation, radiation luminosity. Examples (graphical demonstration of island charge system radiation).
    Relativistic electrodynamics. Derivation of Maxwell's equations from the Hamilton principle, 4-current, the 4-potential, 4-tensor of electromagnetic field, Maxwell's equations in covariant form, invariants of electromagnetic field. Plane electromagnetic wave, the wave 4-vector Doppler effect and aberration, the optical appearance of objects moving at relativistic speed. Examples (using the program package Tensors in Physics for the program Mathematica).
    Relativistic dynamics. Equation of motion of charge in an electromagnetic field mass, energy and momentum, 4-momentum force, 4-force, Lorentz 4-force. Uniformly accelerated motion collisions Compton effect the relationship between mass, energy and momentum the energy-momentum tensor. The movement of charged particles in an external electromagnetic field. Examples (numerical solution to movement of charge in an inhomogeneous magnetic field).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Meeting the criteria for obtaining credit in the tutorial. Requirements for successful completion of the examination shall be communicated by the lecturer at the beginning of the semester.
The course is also listed under the following terms Summer 2014, Summer 2015, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021, Summer 2022, Summer 2023.
  • Enrolment Statistics (Summer 2016, recent)
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