Academic Year 2023/2024 - Teacher: MARCO RUGGIERI

Expected 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

The course will be conducted through traditional classroom lectures.

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 in the course is mandatory.

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

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)

D. J. GriffithsIntroduction to Electrodynamics (Fourth Edition)Cambridge University Press2017978-1108420419
L. D. Landau and E. M. LifsitsFisica Teorica 2: Teoria dei CampiEditori Riuniti Univ. Press2010 978-8864732077

Course Planning

 SubjectsText References
1Delta di Dirac, analisi vettoriale, operatori differenziali, sistemi di coordinate (2 ore)testi 1, 3
2Potenziale elettrostatico, dipolo elettrico, energia elettrostatica (2 ore) testi 1, 3
3Equazione di continuità, potenziale vettore del campo magnetico (2 ore)testi 1, 3
4Campo elettrostatico e magnetostatico a grande distanza, sviluppo in multipoli, applicazioni al calcolo dei momenti magnetici dei nuclei atomici (4 ore)testi 1, 3
5Equazioni di Maxwell per sorgenti dipendenti dal tempo, potenziali per campi dipendenti dal tempo (2 ore)testi 1, 3
6Energia magnetica, conservazione dell'energia e vettore di Poynting, conservazione del momento e tensore degli sforzi del campo elettromagnetico (2 ore)testi 1, 3
7Onde piane, onde sferiche da sorgenti puntiformi, potenziali ritardati (2 ore)testi 1, 3
8Campi elettromagnetici ritardati, radiazione elettromagnetica, radiazione da dipolo elettrico, radiazione da dipolo magnetico (5 ore)testi 1, 3
9Potenziali 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
10Postulati 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
11Meccanica 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

The assessment will be conducted through an oral interview, consisting of four questions. Two of these questions will focus on time-dependent fields and electromagnetic radiation, while the other two will relate to special relativity. In determining the final grade, we will consider the correctness of your responses, as well as your ability to communicate using appropriate technical language and to draw connections with other topics from the course curriculum.

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