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

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 .

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.

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 .

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.

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

f) Maxwell equations. Displacement current.

g ) Solution of Maxwell equations with delayed potentials.

Module 2

Exercises on the topics of Module 1 and Module 2.

a ) Relativity . Transformations of Galileo and their incompatibility with the laws of Maxwell. Invariance of the speed of light. Lorentz transformations. Speed composition . Contraction of lengths and time dilation. Own time. Relativistic dynamics. Mass-energy equivalence. Conservation of the impulse and energy. Shock. Electromagnetism in relativity . Transformations for fields E and B.

b) Waves. The wave equation. Flat and spherical waves. Electromagnetic waves . Propagation rate and polarization states. Conservation of energy and Poynting vector . Quantities of motion of the electromagnetic field. Radiation pressure. Dipole radiation and Larmor formula . Wave propagation in material means. Monochromatic and non-monochromatic waves. Wave packages. Speed 'group and phase.

c) Limits of classical electromagnetism. Photoelectric effect.

d) Radiation of a charged particle.

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

Written and oral exam. The results of the written test is valid for the entire session.

During the course, two midterm tests will be offered (approximately in December and May). If both are passed with a grade higher than 18/30, they will replace the written exam for the summer session.

Specifically, the written exam will consist of 3 problems: one concerning electrostatics, one concerning magnetostatics/electromagnetic induction, and one concerning relativity or electromagnetic waves.

The written exam is graded on a 30-point scale. Each of the three problems is worth 10/30. During the written exam, which lasts 180 minutes, the use of personal notes is allowed. The written exam is considered passed with a grade of 18/30 or higher. Passing the written exam is required in order to access the oral exam. Written exam results are communicated to students via AlmaEsami.

The oral exam lasts 30–40 minutes and is divided into two parts: the first part on the first module and the second part on the second module.

During the oral exam, questions may cover any topic included in the syllabus. The oral exam is also graded on a 30-point scale and is considered passed with a minimum score of 18/30.

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

• 18–21: Limited preparation on a subset of topics, with critical thinking emerging only with help from the instructor.

• 22–25: Good preparation on a wide range of topics, but independent critical thinking is only partially evident.

• 26–29: Good preparation on all topics covered in the course, along with good independence and critical thinking skills.

• 30: Complete preparation and excellent independence and critical thinking ability.

The final grade is the average of the written and oral exam grades. Honors (lode) are awarded in cases of excellent preparation and the ability to make connections between different parts of the course.

The grade can be refused up to two times, in accordance with the decisions of the Degree Program Board (CdS). If the grade is refused, the written exam must be taken again.

Office hours

See the website of Annalisa Bonafede

See the website of Francesca Pozzi

See the website of Federico Marulli