Physics, First Cycle
Educational Physics
3 year
Hours per week – 1. semester:

Enrollement status.

Final examination pending on succesfully completed numerical exercises.

Content (Syllabus outline)

Electrostatics: Coulomb's law. Electric charges and their distribution. Electric field, lines of force and Gauss' theorem. Electric potential. Poisson's equation and Green's function. Dirac's delta function. Electrostatic energy and multipole expansion.

Magnetostatocs: Ampere's law. Electric current and its density. Magnetic filed and its lines of force. Magnetic potential. Biot-Savarat's law.

Magnetostatic energy and multipole expansion. Faraday induction and quasistatic fields.

Maxwell's equations: Maxwell7s equations. Conservation laws for electromagnetic fields. Energy density and Poynting vector.

Electromagnetic field in matter: Frequency dependent dielectric function and models of dielectric relaxation.

Electromagnetic potentials and radiation: Electromagnetic potentials, Hertz theory of EM radiation, Electric dipole radiation.

Special theory of relativity: Lorentz transformas. Invariance of Maxwell's equations to Lorentz transforms. Minkowski space.

Electromagnetic filed tensor and covariant form of Maxwell's equations..


H. J.W. Muller-Kirsten, Electrodynamics - an introduction including quantum effects. World Scientific, 2004.
C. A. Brau, Modern problems in classical electrodynamics. Oxford University Press, 2004.
L.D. Landau , E.M. Lifshitz, Classical theory of fileds. 4th ed., Butterworth-Heinemann, 1980.
E.M. Lifshitz, L.D. Landau, L P Pitaevskii, Electrodynamics of Continuous Media. 2nd ed., Butterworth-Heinemann, 1984.
R. Podgornik in A. Vilfan; Elektromagnetno polje, DMFA založništvo, Ljubljana (2012).

Objectives and competences

Goals: Discussion of Maxwell's equations of the electromagnetic field as well as with their covariant formiulation and their consequences.

Acquired competence: Theoretical understanding.

Modelling and solving the models of physical systems.

In depth knowledge of the electromagnetic field.

Acquired capacity to do independent litarature search.

Intended learning outcomes

Knowledge and understanding:

Knowledge of the Maxwell's equations and theit basic consequences, of their symmetries and the covariant form of electrodynamics.

Learning and usage of the covariant formalism.


Learn the vector and tensor analysis as well as the theory of partial differential equations in the classical field theory.


Reduction of the various electromagnetic field phenomena to the consequences of the Maxwell's equations.

Portable competences – not connected with a single subject

The use of vector and tensor analysis in physics. Analysis of the basic equations of the classical theory of fields and derivation of their consequences.

Learning and teaching methods

Lectures, numerical exercices, homeworks and consultations.

Lecturer's references

S. M. Hasheimi, U. Jagodic, M. R. Mozaffari, M. R. Ejtehadi, I. Musevic, and M. Ravnik, Fractal nematic colloids, Nature Commun. 8, 12106-1-14026-9 (2017)

J. Aplinc, M. Stimulak, S. Copar and M. Ravnik, Nematic liquid crystal gyroids as photonic crystals, Liq. Cryst. 43, 2320 (2016)

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer and I. Muševič, Light-controlled topological charge in a nematic liquid crystal, Nature Phys. 11, 183 (2015)

L. Giomi, Z. Kos, M. Ravnik, and A. Sengupta, Cross-talk between topological defects in different fields revealed by nematic microfluidics, Proc. Natl. Acad. Sci. 114, E5771-E5777 (2017)

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I.I. Smalyukh Mutually tangled colloidal knots and induced defect loops in nematic fields, Nature Mater. 13, 258 (2014)