UČNI NAČRT PREDMETA/COURSE SYLLABUS Predmet: Elektromagnetno polje

Course title: Elektromagnetic field

Študijski programi in stopnja Študijska smer Letnik Semestri

Fizika, prva stopnja, univerzitetni Fizika (smer) 3. letnik Zimski

Univerzitetna koda predmeta/University course code: F0224

Predavanja Seminar Vaje Klinične vaje Druge oblike študija

Samostojno delo

ECTS

45 0 30 0 0 135 7

Nosilec predmeta/Lecturer: Miha Ravnik

Vrsta predmeta/Course type: obvezni/compulsory

Jeziki/Languages: Predavanja/Lectures: Slovenščina

Vaje/Tutorial: Slovenščina

Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti:

Prerequisites:

Vpis v letnik. Opravljen izpit iz vaj kot pogoj za pristop k ustnemu izpitu.

Enrollement status. Final examination pending on succesfully completed numerical exercises.

Vsebina: Content (Syllabus outline):

Elektrostatika: Coulombov zakon. Električni naboji in njihove porazdelitve. Električno polje, silnice in Gaussov izrek. Električni potencial. Poissonova enačba in Greenova funkcija. Diracova delta funkcija. Elektrostatska energija in multipolni razvoj. Magnetostatika: Amperov zakon. Električni tok in njegova gostota. Magnetno polje in silnice. Magnetni potencial. Biot-Savartov zakon. Magnetostatska energija in multipolni razvoj. Faradayeva indukcija in kvazistatična polja. Maxwellove enačbe: Maxwellove enačbe. Ohranjevalni zakoni za elektromagnetno polje. Gostota energije in Poyntingov vektor. Elektromagnetno polje v snovi: Frekvenčno odvisna dielektrična funkcija in modeli dielektrične relaksacije. Elektromagnetni potenciali in sevanje: Elektromagnetni potenciali, umeritvene transformacije in Riemann-Sommerfeldove enačbe. Lienard-Wiechertovi potenciali in sevanje. Radiacijski del polja in sevanje. Posebna teorija relativnosti: Lorentzove transformacije. Invariantnost Maxwellovih enačb na Lorentzove transformacije. Prostor Minkowskega. Tenzor elektromagnetnega polja in kovarianten zapis Maxwellovih enačb.

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 potential, gauge transform and Riemann-Sommerfeld equations. Lienard- Wiechert potentials and radiation. Radiation fields and 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..

Temeljna literatura in viri/Readings:

1. H. J.W. Muller-Kirsten, Electrodynamics - an introduction including quantum effects. World Scientific, 2004. 2. C. A. Brau, Modern problems in classical electrodynamics. Oxford University Press, 2004. 3. L.D. Landau , E.M. Lifshitz, Classical theory of fileds. 4th ed., Butterworth-Heinemann, 1980. 4. E.M. Lifshitz, L.D. Landau, L P Pitaevskii, Electrodynamics of Continuous Media. 2nd ed., Butterworth-

Heinemann, 1984. 5. R. Podgornik in A. Vilfan; Elektromagnetno polje, DMFA založništvo, Ljubljana (2012).

Cilji in kompetence: Objectives and competences:

Cilji: Seznanitev z Maxwellovimi enačbami elektromagnetnega polja in njihovimi posledicami ter s kovariantno formulacijo elektrodinamike. Kompetence: Teoretično razumevanje. Sposobnost modeliranja in reševanja fizikalnih problemov. Globlje poznavanje teorije elektromagnetnega polja. Sposobnost iskanja po strokovni literaturi.

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.

Predvideni študijski rezultati: Intended learning outcomes:

Znanje in razumevanje: Poznavanje Maxwellovih enačb in njihovih osnovnih posledic, njihovih simetrij in kovariantne formulacije elektrodinamike. Poznavanje kovariantnega zapisa. Uporaba Uporaba vektorske in tenzorske analize ter teorije parcialnih diferencialnih enačb v klasični teoriji polja. Refleksija Redukcija različnih fenomenov elektromagnetizma na posledice Maxwellovih enačb. Prenosljive spretnosti - niso vezane le na en predmet Uporaba vektorske in tenzorske analize v fiziki. Analiza osnovnih enačb klasične teorije polja in njihovih posledic.

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

Metode poučevanja in učenja: Learning and teaching methods:

Predavanje, vaje, domače naloge in konzultacije. Lectures, numerical exercices, homeworks and consultations.

Načini ocenjevanja: Delež/Weight Assessment:

2 kolokvija iz vaj ali pisni izpit 50,00 %

2 testa iz teorije ali ustni izpit. 50,00 %

Ocene: 5 (negativno), 6-10 (pozitivno) (po Statutu UL).

Reference nosilca/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)