ELETTRODINAMICA CLASSICA
Academic Year 2026/2027 - 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
If the course is delivered in blended or remote mode, appropriate adjustments may
be made to the above, in order to ensure consistency with the syllabus.
All the communications related to the course will take place on the Telegram channel Elettrodinamica 26/27.
Information for students with disabilities and/or learning disabilities (LD).
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
Attendance is strongly recommended (in accordance with the University regulations).
Detailed Course Content
Mathematical Preamble
Dirac delta function, vector analysis, differential operators, coordinate systems, Fourier transforms, Helmholtz theorem.
Invariances of Electrodynamics and Electromagnetic Potentials
Gauge invariance of electrodynamics, electromagnetic potentials, formulation of electrodynamics in terms of potentials. Electrostatic potential. Vector potential. Invariance of electrodynamics under spacetime transformations. Conservation of energy and momentum in electrodynamics. Maxwell stress tensor. Applications to field dynamics in relativistic-energy collisions.
Review of Electrostatics and Magnetostatics
Green's function method for solving Poisson's equation. Far-field electrostatic fields and multipole expansion, applications to the calculation of the magnetic moments of atomic nuclei. Debye screening and its applications to stellar and relativistic plasma physics.
Time-Dependent Fields
Potentials and fields produced by time-dependent sources. Spherical waves from point sources, retarded potentials.
Electromagnetic Radiation
Retarded electromagnetic fields, electromagnetic radiation, electric dipole radiation, magnetic dipole radiation. Applications to magnetic dipole radiation emitted by pulsars. Spectral decomposition of retarded potentials.
Covariant Formulation of Electrodynamics
Analytical mechanics of a point charge, Lorentz transformations of the electromagnetic field, covariant form of Maxwell's equations, electromagnetic field tensor, field invariants, electromagnetic field action, energy-momentum tensor. Proca Lagrangian, Maxwell-Proca equations, applications of an effective photon mass.
Fields of Moving Charges
Liénard-Wiechert potentials, fields of a charge moving at constant velocity. Electromagnetic fields in heavy-ion collisions. Radiation from accelerated charges, bremsstrahlung, synchrotron radiation, applications to nuclear physics and astrophysics. Examples of the motion of a relativistic charged particle in uniform electric and magnetic fields.
Electrodynamics in Material Media
Maxwell's equations in material media, response functions in dielectric and conducting materials, Kramers-Kronig relations, an introduction to selected classical models. Electromagnetic waves in dielectrics and metals, phase and group velocities, scattering of electromagnetic radiation.
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 | Dirac delta, vector analysis, differential operators, coordinate systems. Fourier transforms. Helmholtz theorem. (2 hours) | testi 1, 3 |
| 2 | Gauge invariance. Formulation of electrodynamics in terms of potentials. Conservation laws. Stress tensor. Potentials for time-dependent sources. Electrostatic potential, vector potential, invariance of electrodynamics under spacetime transformations, applications to field dynamics in relativistic-energy collisions. (8 hours) | testi 1, 3 |
| 3 | Electrostatic and magnetostatic fields at large distances, multipole expansion, applications to the calculation of magnetic moments of atomic nuclei. Green’s function method for solving Poisson’s equation, Debye screening and applications to stellar and relativistic plasmas. (4 hours) | testi 1, 3 |
| 4 | Spherical waves from point sources, retarded potentials. (2 hours) | testi 1, 3 |
| 5 | Retarded electromagnetic fields, electromagnetic radiation, electric dipole radiation, magnetic dipole radiation. Applications to magnetic dipole radiation emitted by pulsars, spectral decomposition of retarded potentials. (5 hours) | testi 1, 3 |
| 6 | Liénard–Wiechert potentials, fields of a charge moving at constant velocity, radiation from accelerated charges, bremsstrahlung, synchrotron radiation, applications to nuclear physics and astrophysics. Explicit application to relativistic heavy-ion collisions and examples of the motion of a relativistic charged particle in uniform electric and magnetic fields. (6 hours) | testi 1, 3 |
| 7 | Analytical mechanics of a point charge, Lorentz transformations of the electromagnetic field, covariant formulation of Maxwell’s equations, action of the electromagnetic field. Electromagnetic field tensor, field invariants, energy–momentum tensor, Proca Lagrangian, Maxwell–Proca equations, applications of an effective photon mass. (6 hours) | testi 2, 3 |
| 8 | Electrodynamics in material media: Maxwell’s equations in matter, response functions in dielectric and conducting materials, Kramers–Kronig relations, an introduction to selected classical models, electromagnetic waves in dielectrics and metals, phase and group velocities, scattering of electromagnetic radiation. (9 hours) | testo 1 |
Learning Assessment
Learning Assessment Procedures
To ensure equal opportunities and in compliance with applicable laws, interested students may request a personal interview to plan any compensatory and/or extenuating measures, based on their educational objectives and specific needs. Students may also contact the CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or Learning Disabilities) contact teacher in the Department of Physics.
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