CLASSIC ELECTRODYNAMICS

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.

The course will be conducted through frontal lessons.

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 is mandatory.

Mathematical Preamble

Dirac delta, vector analysis, differential operators, coordinate systems

Recap 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 dipoles, radiation from magnetic dipoles.

Fields of moving charges

Lienard-Wiechert potentials, fields of a charge in uniform motion, radiation from accelerated 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, invariant relativistic 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

1. M. Maggiore, A Modern Introduction to Classical Electrodynamics, OUP Oxford (2023)

2. D. J. Griffiths, Introduction to Electrodynamics (Fourth Edition), Cambridge University Press (2017)

3. L. D. Landau and E. M. Lifsits, Fisica Teorica 2: Teoria dei Campi, Editori Riuniti Univ. Press (2010)

Other texts suggested for consultation

A. Zangwill, Modern Electrodynamics, Cambridge University Press (2013)

J. D. Jackson, Classical Electrodynamics International Adaption (Third Edition), John Wiley & Sons (2021)

M. Schwartz, Principles of Electrodynamics, Dover Publications (1987)

The evaluation will take place through an oral examination, consisting of four questions, two of which will be related to time-dependent fields and electromagnetic radiation, and two on special relativity. Among the criteria for determining the final grade, correctness of the answers will be assessed, as well as the student's ability to communicate using appropriate technical language and to make connections with other topics covered in the course.

Maxwell's Equations for Time-Dependent Sources

Retarded Potentials

Fields Produced by a Charge in Uniform Rectilinear Motion

Radiation Produced by a Charge in Uniform Circular Motion

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