# ELECTROMAGNETIC FIELDS

OVERVIEW

The undergraduate course “Electromagnetic Fields” introduces and develops basic ideas related to the electromagnetic fundamental laws, to electromagnetic propagation, to the ways lumped and distributed circuits work. Its aim is to provide the students with the essential tools for understanding the electromagnetic phenomena and the many practical applications of electromagnetic fields.

## AIMS AND CONTENT

LEARNING OUTCOMES

The target of the course is to provide the students with the essential tools for understanding the electromagnetic phenomena and the many practical applications of electromagnetic fields.

AIMS AND LEARNING OUTCOMES

The course provides the students the basic notions related to electromagnetic fields. During the lectures the electromagnetic fundamental laws, the extensions of the laws of conservation of energy and momenta to electromagnetics, the simplest electromagnetic waves and the basic principles of the theory of lumped and distributed circuits are presented. The course aim is to provide the essential tools for understanding the electromagnetic phenomena and the many practical applications of electromagnetic fields.

Al the end of the course, the student will be able to describe the main concepts of electrodynamics in the presence of charges in vacuum and in the presence of ponderable media. They will also be able to solve simple electromagnetic problems related to important practical applications.

Teaching methods

All teaching activities are presented by the teacher. According to the choice of the Bachelor of Science Course in Computer Engineering the activities will be taught at a distance.

SYLLABUS/CONTENT

1. Course organization, motivation and applications. Some comments on Newtonian and relativistic physics (2; 2)

2. Quantization of the charge and of the electromagnetic field: the role of classical relativistic electrodynamics in modern physics; some links between classical relativistic and quantum electrodynamics in simple cases; some properties of photons; number and properties of photons involved in many engineering applications (2; 4)

3. Recalling some prerequisites: Lorentz force; different models for electric charge distributions; electric current and electric current density; conservation of charge; Maxwell's equations in the presence of charges in vacuum in integral form (2; 6)

4. Exercises related to scalar and vector fields, circulations, fluxes, differential operators, international system of units (for electromagnetic quantities); fundamental equations in the presence of charges in vacuum in differential form (2; 8)

5. Physics of matter for drift currents, electric and magnetic polarizations (2; 10)

6. Electric polarization of matter: from elementary distributions of point charges to electric dipole moment density (electric polarization or dipole moment per unit volume) (2; 12)

7. Electric polarization of matter: surface and volume charge densities equivalent to the distribution of dipoles; macroscopic effect of polarization-charge densities; generalization of Gauss theorem; electric displacement; first generalization of Ampere-Maxwell law (2; 14)

8. Magnetic polarization of matter: magnetic dipole moment density per unit volume (magnetic polarization or magnetic dipole moment per unit volume); linear and surface current densities equivalent to the distribution of magnetic dipoles; macroscopic effects of polarization-current densities; final form of Maxwell's equations (integral and differential forms) (2; 16)

9. First consequences of the way electric circuits works (2; 18)

10. Some comments on the constitutive relationships (2; 20)

11. Boundary conditions at motionless interfaces between different media: conditions for the normal components of the electric displacement, of the magnetic induction and of the Poynting vector; conditions for the tangential parts of the electric and magnetic fields (2; 22)

12. Extension to electromagnetic phenomena of the principle of energy conservation: physical meaning of the terms appearing in Poynting theorem involving Poynting vector, impressed and drift current densities (2; 24)

13. Physical meaning of the terms appearing in Poynting theorem involving the induction and the electric displacement fields (2; 26)

14. Exercises and practial implications: exchange between electromagnetic energy and mechanical or thermal energy; Nichols' disk; Joule's effect in a cylindrical conductor (2; 28)

15. Poynting theorem for time-harmonic fields (2; 30)

16. Exercises: power losses due to Joule effect and to dielectric losses; thermal effects in microwave ovens; field amplitudes radiated by isotropic antennas in a lossless and homogeneous medium (2; 32)

17. Conservation of momentum in the presence of charged particles and electromagnetic fields; a comment on the conservation of the angular momentum (2; 34)

18. Uniqueness theorem for the electromagnetic field: importance of boundary conditions and of initial conditions (2; 36)

19. Practical implications: waveguides, radiation problems, electromagnetic scattering problems (2; 38)

20. Wave equation; wave equation in one space dimension: general form of its solution (2; 40)

21. Electromagnetic plane waves: TEM waves; general expressions for the electric and magnetic fields; speed of light as the velocity of propagation of electromagnetic plane waves (2; 42)

22. Monochromatic plane waves; wavelength, wavevector, polarization of time-harmonic vectors and vector fields and its practical consequences (2; 44)

23. Practical implications: attenuation; skin depth; velocity of propagation; some comments on the effects of dispersive media on the propagation of digital signals (2; 46)

24. Introduction to distributed circuits (transmission lines): lumped models circuits vs distributed model circuits; their importance in practice (2; 48)

RECOMMENDED READING/BIBLIOGRAPHY

- S. Bobbio, E. Gatti, Elementi di elettromagnetismo, Bollati Boringhieri, 1991
- G. Conciauro, L. Perregrini, Fondamenti di onde elettromagnetiche, McGraw-Hill, 2003
- J. D. Jackson, Classical electrodynamics, Wiley, 1999
- D. Pescetti, Elettromagnetismo, Piccin, 1985

The teacher has written the lecture notes for this course. They are available for all students.

## TEACHERS AND EXAM BOARD

**Ricevimento:** Monday, from 5 to 6 p. m., third floor, Via Opera Pia 11a, or by appointment.

Exam Board

MIRCO RAFFETTO (President)

ANDREA RANDAZZO

MATTEO PASTORINO

ALESSANDRO FEDELI

GIAN LUIGI GRAGNANI (President Substitute)

## LESSONS

Teaching methods

All teaching activities are presented by the teacher. According to the choice of the Bachelor of Science Course in Computer Engineering the activities will be taught at a distance.

## EXAMS

Exam description

The final exam is oral. All students will be asked three questions, of which at least one theoretical and one presented as an exercise.

Assessment methods

At the end of the course the student should show to have understood the basic principle of electrodynamics in the presence of charges in vacuum or in matter and to be able to solve simple problems.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

04/06/2021 | 00:01 | GENOVA | Esame su appuntamento | |

10/06/2021 | 10:00 | GENOVA | Orale | |

16/06/2021 | 10:00 | GENOVA | Orale | |

23/06/2021 | 00:01 | GENOVA | Esame su appuntamento | |

30/06/2021 | 10:00 | GENOVA | Orale | |

01/07/2021 | 10:00 | GENOVA | Orale | |

15/07/2021 | 00:01 | GENOVA | Esame su appuntamento | |

23/07/2021 | 10:00 | GENOVA | Orale | |

23/07/2021 | 10:00 | GENOVA | Orale | |

06/09/2021 | 10:00 | GENOVA | Orale | |

15/09/2021 | 10:00 | GENOVA | Orale | |

16/09/2021 | 00:01 | GENOVA | Esame su appuntamento |