Unit PHYSICS II
- Course
- Mathematics
- Study-unit Code
- 55126209
- Curriculum
- In all curricula
- Teacher
- Maurizio Biasini
- Teachers
-
- Maurizio Biasini
- Hours
- 63 ore - Maurizio Biasini
- CFU
- 9
- Course Regulation
- Coorte 2025
- Offered
- 2026/27
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Sector
- FIS/01
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The course introduces the fundamental concepts of classical electromagnetism and waves, with particular attention to the mathematical formulation of physical laws and the solution of simple problems.
The following topics will be covered: electric field, electric potential, Gauss’s law, capacitors, electric current, direct-current circuits, magnetic field, Lorentz force, Ampère’s law, electromagnetic induction, Maxwell’s equations in elementary form, electromagnetic waves, and an introduction to physical optics. - Reference texts
- D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, Casa Editrice Ambrosiana / Zanichelli.
Teaching material provided by the instructor. - Educational objectives
- The aim of the course is to provide students with a basic knowledge of classical electromagnetism and waves, while also developing their ability to use elementary mathematical tools to describe physical phenomena.
At the end of the course, students should be able to:
know the main electric and magnetic quantities;¿understand the concept of electric field and magnetic field;¿apply Coulomb’s law and Gauss’s law in simple situations;¿calculate the electric potential in elementary configurations;¿describe the behaviour of capacitors and simple electric circuits;¿understand the physical meaning of electric current, resistance, and Ohm’s law;¿calculate the magnetic force on charges and currents;¿apply Ampère’s and Faraday’s laws in simple cases;¿understand the meaning of electromagnetic induction;¿recognize the role of Maxwell’s equations in the unified description of electromagnetic phenomena;¿understand, at an elementary level, the nature of electromagnetic waves;¿solve basic exercises, checking units of measurement, signs, and orders of magnitude. - Prerequisites
- Basic knowledge of general physics and mathematics is required, in particular:
elementary kinematics and dynamics;¿energy, work, and conservation of energy;¿algebra and trigonometry;¿elementary functions;¿derivatives and integrals in one variable;¿elementary notions of vectors;¿elements of analytic geometry.
Introductory knowledge of multiple integrals, vector fields, and elementary differential operators is useful but not essential. - Teaching methods
- The course will be delivered through lectures and exercise sessions.
The theoretical lectures will introduce the fundamental physical concepts, trying to connect them to their mathematical formulation. The exercise sessions will be devoted to the guided solution of simple and progressive problems.
During the course, the following will be used:
elementary physical examples;¿diagrams and graphical representations of fields;¿numerical exercises;¿symbolic exercises;¿mathematical reminders when necessary;¿discussion of the most common mistakes in problem solving.
Particular attention will be devoted to conceptual understanding, avoiding a purely mnemonic approach to formulas. - Other information
- Attendance is recommended, especially in order to follow the gradual development of the topics and the solution of exercises.
The teaching material used during the course may be made available on the platform indicated by the instructor. Students are encouraged to regularly work through the proposed exercises.
The instructor may indicate during the course any topics to be studied in greater depth or, conversely, topics to be treated only at an introductory level. - Learning verification modality
- Assessment will consist of a written test, possibly supplemented by an oral examination, if required.
The written test will consist of exercises and basic theoretical questions aimed at assessing:
knowledge of the fundamental laws of electromagnetism;¿the ability to correctly set up a physical problem;¿appropriate use of formulas;¿correct handling of vector and scalar quantities;¿the ability to perform simple calculations;¿checking of units of measurement;¿understanding of the physical meaning of the results obtained.
The oral examination, if required, will assess the understanding of the main concepts, clarity of explanation, and the ability to connect the different topics of the course.
The final evaluation will take into account scientific correctness, reasoning ability, clarity of presentation, and the correct use of physical and mathematical language. - Extended program
- 1. Mathematical and physical reminders
Scalar and vector quantities. Operations with vectors. Scalar product and vector product. Scalar fields and vector fields. Introduction to gradient, divergence, and curl, presented in an operational way. Line, surface, and volume integrals in simple cases. Review of energy, force, and work.
2. Electric field
Electric charge. Properties of charge. Conductors and insulators. Coulomb’s law. Principle of superposition. Electric field generated by a point charge. Electric field produced by discrete charge distributions. Introduction to continuous charge distributions.
Electric field lines. Physical interpretation of the electric field. Motion of a charge in a uniform electric field.
3. Gauss’s law
Flux of the electric field. Closed surfaces. Gauss’s law in integral form. Physical meaning of Gauss’s law. Simple applications to symmetric charge distributions: sphere, infinite plane, infinite wire, conductor in electrostatic equilibrium.
Relationship between Gauss’s law and Coulomb’s law in simple cases.
4. Electric potential and electrostatic energy
Work of the electric force. Electric potential energy. Electric potential. Potential difference. Relationship between electric field and potential. Equipotential surfaces.
Potential generated by a point charge and by simple charge distributions. Energy of a system of charges. Motion of a charge between points at different potential.
5. Conductors and capacitors
Conductors in electrostatic equilibrium. Electric field inside a conductor. Distribution of charge on the surface. Capacitance. Parallel-plate capacitor. Capacitors in series and in parallel. Energy stored in a capacitor. Introduction to dielectrics.
6. Electric current and circuits
Electric current. Current density. Electrical resistance. Ohm’s law. Resistivity and conductivity. Electric power and Joule effect.
Direct-current circuits. Resistors in series and in parallel. Ideal and real generators. Kirchhoff’s laws. RC circuits: charging and discharging of a capacitor, time constant, and qualitative behaviour of the quantities over time.
7. Magnetic field
Introduction to the magnetic field. Lorentz force on a moving charge. Motion of a charge in a uniform magnetic field. Magnetic force on a current-carrying wire. Magnetic moment of a loop.
Magnetic field lines. Differences between electric field and magnetic field.
8. Sources of the magnetic field
Magnetic field produced by currents. Biot-Savart law in simple cases. Field produced by an infinite straight wire. Field at the centre of a circular loop. Ampère’s law. Elementary applications of Ampère’s law: straight wire, long solenoid, ideal toroid.
9. Electromagnetic induction
Flux of the magnetic field. Faraday-Neumann law. Lenz’s law. Induced electromotive force. Induced currents. Simple examples of induction: loop in a variable magnetic field, variation of area, motion of a conductor in a magnetic field.
Introduction to self-induction and inductance. Energy stored in a magnetic field. Qualitative treatment of RL circuits.
10. Maxwell’s equations
Review of the fundamental laws of electromagnetism. Gauss’s law for the electric field. Gauss’s law for the magnetic field. Faraday’s law. Ampère-Maxwell law. Displacement current.
Presentation of Maxwell’s equations in integral form. General physical meaning: unification of electric and magnetic phenomena. Introduction to the differential form, only as a connection with vector analysis.
11. Electromagnetic waves
Origin of electromagnetic waves. Propagation in vacuum. Speed of light. Relationship between electric field, magnetic field, and direction of propagation. Energy carried by an electromagnetic wave. Electromagnetic spectrum.
Introduction to polarization, intensity, and radiation pressure.
12. Introduction to physical optics
Wave nature of light. Interference. Diffraction. Double-slit experiment. Introductory treatment of the diffraction grating. Connection between wavelength, frequency, and colour. Simple applications and qualitative interpretation of the observed phenomena.
13. Exercises and applications
Solution of simple problems on electric field, potential, Gauss’s law, capacitors, circuits, magnetic field, induction, and electromagnetic waves.
The exercises will be chosen to strengthen the understanding of the fundamental concepts and the correct use of basic mathematical tools.