Classical Electrodynamics
A.Y. 2024/2025
Learning objectives
Starting from Maxwell's equations, advanced knowledge of electromagnetism and special relativity is provided. The generation and propagation of electromagnetic waves in vacuum and in dielectric media, the covariant formalism of the electromagnetic field and the emission of radiation from accelerated charges are studied.
Expected learning outcomes
At the end of the course the student will acquire the following skills:
1. will be able to describe the phenomenology of dispersion and absorption of radiation in a linear medium;
2. will be able to describe the phenomenology of radiation emission by distributions of accelerated charges;
3. will be able to describe the relativistic dynamics of charged particles in electromagnetic fields;
4. will be able to tackle specific electrodynamic problems in different fields of physics (accelerators, particle physics, astrophysics) concerning the relativistic dynamics of charged particles and radiation emission;
5. will be able to follow field theory courses in a profitable way using the acquired knowledge of relativistic electrodynamics.
1. will be able to describe the phenomenology of dispersion and absorption of radiation in a linear medium;
2. will be able to describe the phenomenology of radiation emission by distributions of accelerated charges;
3. will be able to describe the relativistic dynamics of charged particles in electromagnetic fields;
4. will be able to tackle specific electrodynamic problems in different fields of physics (accelerators, particle physics, astrophysics) concerning the relativistic dynamics of charged particles and radiation emission;
5. will be able to follow field theory courses in a profitable way using the acquired knowledge of relativistic electrodynamics.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Responsible
Lesson period
First semester
Course syllabus
1) Maxwell equations, conservation laws, electromagnetic waves.
Maxwell equations. Scalar potential and vector potential. Gauge transformations; Lorenz and Coulomb gauge. Green functions for the wave equation. Retarded solutions for fields. Poynting theorem and conservation of energy, momentum and angular momentum for a system of charged particles and electromagnetic fields. Poynting theorem for harmonic fields; field definition of impedance. Electromagnetic waves. Plane waves in lossless and and in conductive/dissipative media. Brief notes on the optical properties of metamaterials. Reflection and refraction at a plane surface between two media. Total internal reflection. Dispersive characteristics of dielectrics, conductors and plasmas. Simplified model of wave propagation in the ionosphere. Group speed and spreading of a pulse in a dispersive medium. Causality in the relationship between D and E; Kramers-Kronig relations. Propagation in waveguides: TEM, TE and TM modes. Fields and radiation of a localized oscillating source: electric dipole, magnetic dipole and electric quadrupole. Thomson and Rayleigh diffusion.
2) The theory of special relativity, dynamics of relativistic particles and electromagnetic fields.
Lorentz transformations and basic kinematics of special relativity. Mathematical properties of space-time. Covariance of electrodynamics. Transformation of electromagnetic fields. Lagrangian and Hamiltonian of a particle in external electromagnetic fields. Quadratic invariants of the electromagnetic field. The fields generated by a charge in uniform straight motion. Motion of a charged particle in static and uniform electric and magnetic fields. Lagrangian of the electromagnetic field. Energy-moment tensor of the electromagnetic field and conservation laws in covariant form.
3) Emission of radiation from charged particles in accelerated motion
Liénard-Wiechert potentials and fields of a point charge. Total power radiated by an accelerated charge. Angular and frequency distribution of the radiation emitted by an accelerated charge. Energy loss by radiation in linear and circular accelerators.
Maxwell equations. Scalar potential and vector potential. Gauge transformations; Lorenz and Coulomb gauge. Green functions for the wave equation. Retarded solutions for fields. Poynting theorem and conservation of energy, momentum and angular momentum for a system of charged particles and electromagnetic fields. Poynting theorem for harmonic fields; field definition of impedance. Electromagnetic waves. Plane waves in lossless and and in conductive/dissipative media. Brief notes on the optical properties of metamaterials. Reflection and refraction at a plane surface between two media. Total internal reflection. Dispersive characteristics of dielectrics, conductors and plasmas. Simplified model of wave propagation in the ionosphere. Group speed and spreading of a pulse in a dispersive medium. Causality in the relationship between D and E; Kramers-Kronig relations. Propagation in waveguides: TEM, TE and TM modes. Fields and radiation of a localized oscillating source: electric dipole, magnetic dipole and electric quadrupole. Thomson and Rayleigh diffusion.
2) The theory of special relativity, dynamics of relativistic particles and electromagnetic fields.
Lorentz transformations and basic kinematics of special relativity. Mathematical properties of space-time. Covariance of electrodynamics. Transformation of electromagnetic fields. Lagrangian and Hamiltonian of a particle in external electromagnetic fields. Quadratic invariants of the electromagnetic field. The fields generated by a charge in uniform straight motion. Motion of a charged particle in static and uniform electric and magnetic fields. Lagrangian of the electromagnetic field. Energy-moment tensor of the electromagnetic field and conservation laws in covariant form.
3) Emission of radiation from charged particles in accelerated motion
Liénard-Wiechert potentials and fields of a point charge. Total power radiated by an accelerated charge. Angular and frequency distribution of the radiation emitted by an accelerated charge. Energy loss by radiation in linear and circular accelerators.
Prerequisites for admission
Knowledge of the concepts and methods introduced in the Bachelor's Degree in Physics, in particular in the courses of Classical Mechanics, Electromagnetism and Analysis.
Teaching methods
Lectures using blackboard and slides.
Teaching Resources
J. D. Jackson, "Classical Electrodynamics", 3rd ed., John Wiley & Sons (1999) [Italian edition: J. D. Jackson, "Elettrodinamica Classica", II ed., Zanichelli, 2001].
Notes on the Ariel platform.
Other textbooks:
L. D. Landau, E. M. Lifshitz, "The Classical Theory of Fields", 3rd ed., Pergamon, 1971
E. M. Purcell and J. D. Morin, "Electricity and magnetism", 3rd ed., Cambridge University Press, 2013
D. J. Griffiths, "Introduction to electrodynamics", 4th ed., Pearson, 2014
Notes on the Ariel platform.
Other textbooks:
L. D. Landau, E. M. Lifshitz, "The Classical Theory of Fields", 3rd ed., Pergamon, 1971
E. M. Purcell and J. D. Morin, "Electricity and magnetism", 3rd ed., Cambridge University Press, 2013
D. J. Griffiths, "Introduction to electrodynamics", 4th ed., Pearson, 2014
Assessment methods and Criteria
Oral exam with questions on the topics covered in class, to check if the teaching objectives have been achieved and the student has acquired the basic knowledge of the subject. The exam typically lasts 45 minutes, with two or more topics covered by the student.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Rome' Massimiliano Gaetano
CORSO B
Responsible
Lesson period
First semester
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Piovella Nicola Umberto Cesare
Professor(s)
Reception:
Friday, 9: 30-12: 30 (by appointment)
office at the Department of Physics