27215 - General Physics 2

Learning outcomes

At the end of the course, the student has the basic knowledge of classical electromagnetism and special relativity as wella s the skills necessary for solving elementary problems.

Course contents

Module 1

1.a) Elements of differential and integral vector calculus. Scalar and vector fields. Gradient operator. Flow and circulation in vector fields. Theorems of Gauss and Stokes .

1.b) Electrostatics. Electric charge. Coulomb's law. Electrical field and electrostatic potential. Field lines and equipotential surfaces. Gauss's law. Poisson equations . Electric dipole. Moments of multipole. Conductor electrostatics. General problem of electrostatics and Laplace equation. Electrostatic energy. Capacitors. Electric field in dielectrics.

1.c) The continuous electric current. Intensity of current and current density . Continuity equation . Laws of Ohm and Joule also in local form. Kirchhoff 's laws .

1.d) The constant magnetic field in the vacuum. Magnetic phenomena. Vector magnetic induction. Biot- Savart law . Laplace formulas. Lorentz force . Flow and circuitation of B. Divergence and rotation of B. Potential vector. Ampere equivalence theorem. Magnetic field in the matter.

1.e) Electromagnetic induction. Faraday's law. Non-conservative electric field. Self-induction and mutual induction. The energy of the magnetic field.

1.f) Maxwell equations. Displacement current.

Module 3

Exercises on the topics of Module 1

Module 2

2.a) Waves. The wave equation. Plane and spherical waves. Mechanical and electromagnetic waves.

2.b) Solution of Maxwell's equations using the retarded potentials.

2.c) Conservation of energy and the Poynting vector. Momentum of the electromagnetic field. Radiation pressure. Propagation velocity and polarization states. Polaroid and birefringent plates. Malus's law. Propagation of waves in material media. Wave packets. Group velocity and phase velocity.

2.d) Limitations of classical electromagnetism. The photoelectric effect and Compton scattering.

2.e) Radiation emitted by a charged particle. Larmor's formula.

2.f) Relativity. Galilean transformations and their incompatibility with Maxwell's equations. Invariance of the speed of light.

Lorentz transformations. Velocity addition. Length contraction and time dilation. Proper time. Relativistic Doppler effect. Relativistic dynamics. Mass–energy equivalence. Conservation of momentum and energy. Collisions. Electromagnetism in special relativity. Transformation laws for the electric (E) and magnetic (B) fields.

2.g) Exercises covering topics 2.a), 2.b), 2.c), 2.d), 2.e), and 2.f).

 

Readings/Bibliography

- Mencuccini, Silvestrini, FISICA Elettromagnetismo e Ottica, Casa Editrice Ambrosiana

- Mazzoldi, Paolo. Fisica Vol. II., EdiSES, 2021.

- Mazzoldi, Nigro.Voci, Fisica Vol II, EdiSES 2019.

- R. Resnick, Introduzione alla relativita' ristretta, Casa Editrice Ambrosiana

 

-G. Balestrino, P. G. Medaglia, S. Sanna, Elettromagnetismo e Onde Guida alla Soluzione degli Esercizi da Mazzoldi, Nigro, Voci - Fisica Mazzoldi, Nigro, Voci - Elementi di Fisica. EdiSES, 2023.

-M. Zani, P. Taroni, L. Duò, Esercizi di Fisica Elettromagnetismo e Onde, Edises 2021.

Teaching methods

Lecture at the blackboard and solution of problems in the classroom

Assessment methods

Starting from the 2026/2027 academic year, the examination is divided into Module 1 + Module 3 and Module 2. Each module consists of a written examination followed by an oral examination.

The written examination for each module is valid only for the current examination session (the written and oral examinations must be completed within the same exam session).

Once a module has been successfully completed (both the written and oral examinations), the result remains valid indefinitely until the other module has also been completed and the final examination grade has been officially recorded.

Each written examination lasts 2 hours.

The written examination consists of 2–3 exercises, one of which is very similar to those covered during lectures or included in the exercise notes provided to students throughout the academic year. During the examination, students are permitted to use a formula sheet consisting of one A4 page.

The written examination is considered passed with a grade of at least 16/30.

The results of the written examination are made available to students through AlmaEsami.

The oral examination lasts approximately 20 minutes for each module.

During the oral examination, students may be asked questions covering any topic included in the course syllabus. The oral examination is graded on a 30-point scale and is considered passed with a minimum grade of 16/30.

The oral examination grade is determined according to the following criteria:

• 16–17: Preparation is limited to a subset of the course topics, and critical thinking skills emerge only partially and with the guidance of the examiner.

• 18–21: Preparation is limited to a subset of the course topics, and critical thinking skills emerge only with the examiner's assistance.

• 22–25: Good preparation on a broad range of topics, but independent critical thinking is demonstrated only to a limited extent.

• 26–29: Good preparation across all course topics, combined with good independence and critical thinking skills.

• 30: Comprehensive preparation together with excellent independence and critical thinking skills.

The final grade for each module is the average of the written and oral examination grades. A module is considered passed with a final grade of at least 16/30.

The final course grade is calculated as the weighted average of the grades obtained in the two modules, using the number of CFU (ECTS credits) assigned to each module as weights. The course is considered passed if the overall final grade is at least 18/30.

Honours (30 cum laude) are awarded only in cases of outstanding preparation and an exceptional ability to connect and integrate the different parts of the course.

In accordance with the regulations of the Degree Programme, a final grade may be declined up to two times. If a student declines the final grade, the written examination must be retaken.

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

 

 

Teaching tools

whiteboard and projector. Teaching material on the "Virtuale" platform.

Office hours

See the website of Annalisa Bonafede

See the website of Francesca Pozzi

See the website of Federico Marulli