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    Relativistic Electrodynamics for Engineers

    A tantárgy neve magyarul / Name of the subject in Hungarian: Relativisztikus elektrodinamika mérnököknek

    Last updated: 2023. április 13.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics

    BSc Electrical Engineering

    Optional subject 
    Course ID Semester Assessment Credit Tantárgyfélév
    VIHVAV26   4/0/0/v 4  
    3. Course coordinator and department Dr. Gyimóthy Szabolcs,
    4. Instructors Szabolcs Gyimóthy, PhD, DSc, dr habil, full professor
    5. Required knowledge Physics, electromagnetic fields, vector calculus
    6. Pre-requisites
    Kötelező:
    NEM ( TárgyEredmény( "BMEVIHVM115" , "jegy" , _ ) >= 2
    VAGY
    TárgyEredmény("BMEVIHVM115", "FELVETEL", AktualisFelev()) > 0)

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

    Ajánlott:
    Introduction to Electromagnetic Fields (VIHVAC03)
    Physics 1 (TE11AX01)
    Physics 2 (TE11AX02) 
    7. Objectives, learning outcomes and obtained knowledge A relativistic formulation of the fundamental laws of electrodynamics; an introduction to the applications of special relativity in electrical engineering.
    8. Synopsis
    Introduction (week 1)
    Subject requirements. Background and brief history of relativity. Basic concepts: reference and coordinate systems. Galilean relativity: equation of motion and its Galilean transform; electromagnetic wave equation and its Galilean transform. 'Aether experiments': Michelson-Morley, Trouton-Noble, Fizeau experiment, Bradley aberration; conclusion of experiments; concept of inertial frame.
     
    Basic phenomena of special relativity expalined by simple mathematical tools (weeks 2-4)
    Optical Doppler effect and its approximation, Ives-Stillwell experiment. New concepts of time: proper time, coordinate time; interpretation of time dilation. Simultaneity and causality. Some basic principles for measuring quantities at rest: time, length, velocity. Length of a moving object, Lorentz contraction, Kennedy-Thorndike experiment, simultaneity and contraction paradoxes. Addition of velocities; explanation of the Fizeau experiment. Relativistic form of the equation of motion: conservation of momentum, relativistic momentum, Newton's second axiom. Obsolete interpretations: rest mass and moving mass, longitudinal and transverse mass; Kaufmann experiment. Mass and energy: kinetic energy of a point of mass; energy at rest; mass and energy of a system (examples). Relationship between energy and momentum; particles with zero mass. Einstein's thought experiment on the E=mc^2 equation.

    Lorentz transformation and space-time (weeks 5-6)
    Derivation of the Lorentz transformation. Minkowsky's spacetime: interval, metrics, "Lorentz rotation" (3D analogy); classification of spacetime intervals (pairs of events). Use of spacetime diagrams: world line, light cone, illustration of Lorentz transformation, length contraction and time dilation. Resolution of the twin paradox. Uniformly accelerating motion, instantaneous rest frame, event horizon.
     
    Electrodynamics in moving reference frames (week 7)
    Introductory example: examining the force acting on a point charge moving parallel to a current-carrying conductor from two points of view. Transforming Maxwell's equations; transformed form of space vectors and source quantities; "semi-relativistic" and non-relativistic approximations.

    Summary of vector and tensor calculus (week 8)
    Classification of coordinate systems, general characteristics of coordinate transformations; matrix of Lorentz transformations, Einstein's convention for summation. four-vectors: definition, examples (velocity, current density). Four-tensors. Vector and tensor algebra: products of tensors, dual tensor, Levi-Civita symbol. Vector and tensor analysis: gradient of scalar field, divergence, rotation and gradient of vector field, divergence and rotation of tensor field, d'Alembert operator.

    Covariant formulation of classical electrodynamics (weeks 9-10)
    Electromagnetics in vacuum: source quantities and continuity; convective current; invariance of charge; electromagnetic tensor, Maxwell's equations; four-potential; electromagnetic energy-momentum, stress-energy tensor. Electromagnetics in matter: polarisation tensor; material properties; differential Ohm's law.

    Special relativity in electrical engineering (weeks 11-14)
    Some applications: the equation of motion of a charged particle; the field of a uniformly moving point charge; the wavenumber four-vector and the Doppler effect; Wilson's experiment; unipolar induction; reflection from a moving mirror; plane wave scattering from a rotating insulating sphere. Consideration of relativistic effects in numerical field simulation: constitutive equations of a moving medium; continuity on the boundary of a moving object. Some devices based on relativistic principle.
    9. Method of instruction Lectures and computer demonstration.
    10. Assessment
    a) During the term: signature. Prerequisite: the completion of a personalised homework assignment, which may include, for example, solving a calculation problem or reading literature.
    b) During the exam period: oral exam based on a chosen topic.
    c.) Preliminary exam: by appointment.
    11. Recaps The homework can be completed during the week of repeats, for a procedure fee.
    12. Consultations

    During the term, at the weekly office hours of the lecturer of the subject (the office hours are available on the department's website); during the examination period, individually, at a pre-arranged time. 

    13. References, textbooks and resources
    Hraskó Péter: A relativitáselmélet alapjai (elektronikusan is), Typotex Kiadó, 2009.
    Simonyi Károly: A fizika kultúrtörténete, Akadémiai Kiadó, 2011.
    Fodor György: Relativisztikus elektrodinamika (kézirat)
    Giber-Sólyom-Kocsányi: Fizika mérnököknek I-II, Műegyetemi Kiadó, 1999.
    Tevan György: Relativisztikus elektrodinamika röviden, Typotex Kiadó, 2013.
    Hraskó Péter: Relativitáselmélet (elektronikusan is), Typotex Kiadó, 2002.
    Feynman-Leighton-Sands: Mai fizika, 2. és 6. kötet, Műszaki Könyvkiadó, 1968.
    Jean Van Bladel: Relativity and Engineering, Springer Berlin, 1984.
    14. Required learning hours and assignment
    Contact lecture56
    Lecture preparation10
    Test preparation
    Homework20
    Written material14
    Exam preparation20
    Total120
    15. Syllabus prepared by
     NamePosition Affiliation 
     Szabolcs Gyimóthyfull professorDept. of Broadband Infocommunications and Electromagnetic Theory