Subject » BMEVIHVAV26
Relativistic Electrodynamics for Engineers
Relativisztikus elektrodinamika mérnököknek
A tantárgyleírás hatályossága
Hatályosság kezdete:
2026. March 21.
Hatályosság vége:
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| Subject name (Hungarian, English) |
Relativisztikus elektrodinamika mérnököknek
Relativistic Electrodynamics for Engineers
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| Subject code | BMEVIHVAV26 | ||||||||||||
| Subject type | — | ||||||||||||
| Training Level | — | ||||||||||||
| Course types and hours (weekly/semester) |
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| Assessment type | vizsga | ||||||||||||
| Credits | 4 | ||||||||||||
| Subject coordinator |
DR. Gyimóthy Szabolcs
position: egyetemi tanár
contact:
gyimothy.szabolcs@vik.bme.hu
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| Responsible department |
Szélessávú Hírközlés és Villamosságtan Tanszék
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| Faculty | Villamosmérnöki és Informatikai Kar | ||||||||||||
| Subject website | — | ||||||||||||
| Primary curriculum type | — | ||||||||||||
| Direct prerequisites – Strong prerequisite | none | ||||||||||||
| Direct prerequisites – Weak prerequisite | none | ||||||||||||
| Direct prerequisites – Parallel prerequisite | none | ||||||||||||
| Direct prerequisites – Milestone prerequisite | none | ||||||||||||
| Direct prerequisites – Exclusion | none |
Objectives
Programme
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.
A relativistic formulation of the fundamental laws of electrodynamics; an introduction to the applications of special relativity in electrical engineering.
Learning outcomes
Ez a tantárgy a KKK rendeletben meghatározott, következő kompetenciák fejlesztését szolgálja:
Knowledge
No learning outcomes recorded.
Skills
No learning outcomes recorded.
Attitudes
No learning outcomes recorded.
Autonomy and responsibility
No learning outcomes recorded.
Oktatási módszertan
Lectures and computer demonstration.
Tanulástámogató anyagok
Online források
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.
Recommended preliminary knowledge for completing the subject
Knowledge type competencies
(azon előzetes ismeretek összessége, amelyek megléte nem kötelező, de a tantárgy eredményes teljesítését nagyban elősegíti)
Physics, electromagnetic fields, vector calculus
Skill type competencies
(azon előzetes képességek és készségek összessége, amelyek megléte nem kötelező, de a tantárgy eredményes teljesítését nagyban elősegíti)
nincs
Recommended (non-compulsory) preliminary competencies
(azon ajánlott (nem kötelező) előzetesen megszerzendő kompetenciák összessége, amelyek jelentősen hozzájárulnak a tantárgy eredményes teljesítéséhez)
Physics, electromagnetic fields, vector calculus
General rules
Requirements:
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.
Additional possibilities:
The homework can be completed during the week of repeats, for a procedure fee.
Assessment methods
In-term assessments
No detailed assessments provided.
Weight of in-term assessments
No weights provided.
Exam-period assessments
No detailed assessments provided.
Weight of exam elements
No weights provided.
Grade calculation
No grade thresholds provided.
Attendance requirements
No attendance requirements provided.
Rules for retake and resubmission
Not provided.
Short description
Not provided.
Detailed description
Not provided.
Recommended courses
Introduction to Electromagnetic Fields (VIHVAC03)
Physics 1 (TE11AX01)
Physics 2 (TE11AX02)
Workload to complete the subject
No workload breakdown provided.
Validity of subject requirements
Requirements valid from:
—
Requirements valid until:
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Curriculum placement
No curriculum placements recorded for this subject version.