CLASSIC ELECTRODYNAMICS
Academic Year 2024/2025 - Teacher: MARCO RUGGIERIExpected Learning Outcomes
The objective of this course is to provide students with the basic knowledge of classical electrodynamics (in both static and dynamic conditions) and special relativity. Although the course is inherently theoretical due to the large number of discussed applications, it is suitable not only for students aiming to specialize in theoretical physics but also as a foundation for those intending to specialize in nuclear and subnuclear physics (both theoretical and experimental), astrophysics, or those planning to work in radiation protection.
The course duration is 42 hours, equivalent to 6 ECTS credits. Points 1 to 8 of the curriculum (21 hours) will be taught by Prof. Ruggieri, while the remaining points (21 hours) will be taught by Prof. Coci.
In more detail, the learning outcomes are as follows:
1. Knowledge and Understanding
- Demonstrate a solid understanding of the fundamental principles of classical electrodynamics.
- Describe concepts related to electromagnetic fields, retarded potentials, and electromagnetic radiation.
- Explain Maxwell's equations and their significance.
2. Application of Knowledge and Understanding
- Apply the laws of electrodynamics to solve complex problems.
- Use the formalism of special relativity to analyze physical situations.
- Apply the principles of classical electrodynamics to applications in nuclear physics, compact stellar object astrophysics, and relativistic nuclear collisions.
3. Drawing Conclusions
- Perform advanced analyses to deduce significant physical results from Maxwell's equations and special relativity.
- Interpret the results of simulations and experiments related to the topics covered.
4. Communicative Skills
- Present fundamental concepts and solutions to problems clearly and effectively through oral and written reports.
- Actively participate in class discussions and presentations on topics related to classical electrodynamics and its applications.
5. Learning Skills
- Demonstrate the ability to learn independently, acquiring new knowledge and further exploring the topics covered in the course.
- Be able to connect classical electrodynamics concepts to recent developments in theoretical and experimental physics.
Course Structure
Required Prerequisites
To successfully follow the course, students should already have a solid foundation in classical physics, particularly in mechanics, electrostatics, and magnetostatics, as well as mathematical analysis (vector analysis and multiple-dimensional integral theorems are important) and algebra (vector operations). These topics will, however, be briefly reviewed at the beginning of the course or whenever they are needed for the development of electrodynamics. Where necessary, references will be made to analytical mechanics (Lagrangian and Hamiltonian formulations). The relativistic formulation in terms of four-tensors, on the other hand, is not required as a prerequisite and will be presented in detail during the course.
Attendance of Lessons
Detailed Course Content
Mathematical Preamble
Dirac delta function, vector analysis, differential operators, coordinate systems
Elements of Electrostatics and Magnetostatics
Electrostatic potential, electric dipole, electrostatic energy, continuity equation, vector potential, far-field and multipole expansion, applications to the calculation of atomic nuclei magnetic moments
Time-Dependent Fields
Maxwell's equations for time-dependent sources, potentials for time-dependent fields, magnetic energy, conservation of energy and Poynting vector, conservation of momentum and stress-energy tensor of the electromagnetic field, plane waves, spherical waves from point sources, retarded potentials
Electromagnetic Radiation
Retarded electromagnetic fields, electromagnetic radiation, radiation from electric dipole, radiation from magnetic dipole
Fields of Moving Charges
Liénard-Wiechert potentials, fields of a charge in uniform motion, radiation from accelerating charges, Bremsstrahlung, synchrotron radiation, applications to nuclear physics and astrophysics
Relativistic Mechanics
Postulates of Special Relativity, four-dimensional interval, Lorentz transformations, analytical mechanics of a relativistic free particle, 4-vectors and 4-tensors, covariance of the laws of nature, relativistically invariant measurements
Covariant Formulation of Electrodynamics
Analytical mechanics of a point charge, Lorentz transformations of the electromagnetic field, covariant form of Maxwell's equations, action of the electromagnetic field
Textbook Information
Testi di riferimento
M. Maggiore, A Modern Introduction to Classical Electrodynamics, OUP Oxford (2023)
D. J. Griffiths, Introduction to Electrodynamics (Fourth Edition), Cambridge University Press (2017)
L. D. Landau and E. M. Lifsits, Fisica Teorica 2: Teoria dei Campi, Editori Riuniti Univ. Press (2010)
Materiale didattico fornito dai docenti
Altri testi di consultazione
J. D. Jackson, Classical Electrodynamics International Adaption (Third Edition), John Wiley & Sons (2021)
| Author | Title | Publisher | Year | ISBN |
|---|---|---|---|---|
| D. J. Griffiths | Introduction to Electrodynamics (Fourth Edition) | Cambridge University Press | 2017 | 978-1108420419 |
| L. D. Landau and E. M. Lifsits | Fisica Teorica 2: Teoria dei Campi | Editori Riuniti Univ. Press | 2010 | 978-8864732077 |
| M. Maggiore | A Modern Introduction to Classical Electrodynamics | OUP Oxford | 2023 | 978-0192867438 |
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Delta di Dirac, analisi vettoriale, operatori differenziali, sistemi di coordinate (2 ore) | testi 1, 3 |
| 2 | Potenziale elettrostatico, dipolo elettrico, energia elettrostatica (2 ore) | testi 1, 3 |
| 3 | Equazione di continuità, potenziale vettore del campo magnetico (2 ore) | testi 1, 3 |
| 4 | Campo elettrostatico e magnetostatico a grande distanza, sviluppo in multipoli, applicazioni al calcolo dei momenti magnetici dei nuclei atomici (4 ore) | testi 1, 3 |
| 5 | Equazioni di Maxwell per sorgenti dipendenti dal tempo, potenziali per campi dipendenti dal tempo (2 ore) | testi 1, 3 |
| 6 | Energia magnetica, conservazione dell'energia e vettore di Poynting, conservazione del momento e tensore degli sforzi del campo elettromagnetico (2 ore) | testi 1, 3 |
| 7 | Onde piane, onde sferiche da sorgenti puntiformi, potenziali ritardati (2 ore) | testi 1, 3 |
| 8 | Campi elettromagnetici ritardati, radiazione elettromagnetica, radiazione da dipolo elettrico, radiazione da dipolo magnetico (5 ore) | testi 1, 3 |
| 9 | Potenziali di Lienard-Wiechert, campi di una carica in movimento con velocità costante, radiazione da cariche accelerate, Bremsstrahlung, radiazione sincrotrone, applicazioni alla fisica nucleare e all'astrofisica (6 ore) | testi 1, 3 |
| 10 | Postulati della Relatività Speciale, intervallo quadridimensionale, trasformazioni di Lorentz, meccanica analitica di una particella libera relativistica, 4-vettori e 4-tensori, covarianza delle leggi della natura, misure relativistiche invarianti (6 ore) | testi 2, 3 |
| 11 | Meccanica analitica di una carica puntiforme, trasformazioni di Lorentz del campo elettromagnetico, forma covariante delle equazioni di Maxwell, azione del campo elettromagnetico (9 ore) | testi 2, 3 |
Learning Assessment
Learning Assessment Procedures
Examples of frequently asked questions and / or exercises
Ecco una possibile traduzione in inglese dei tuoi punti:
Maxwell's Equations for Time-Dependent Sources
Retarded Potentials
Fields Produced by Uniformly Moving Charges
Radiation Produced by Uniform Circular Motion of Charges
Energy and Momentum of the Electromagnetic Field
Action of the Electromagnetic Field
Maxwell's Equations in Covariant Form
Relevant 4-Vectors and 4-Tensors in Electrodynamics