General Physics 2
A.Y. 2024/2025
Learning objectives
The teaching of General Physics 2 has the purpose of providing the basic concepts of electricity and magnetism. Its goal is the discussion of the fundamental laws of Maxwell electromagnetic theory. The electric and magnetic static and time-dependent fields, the general properties of waves and the electromagnetic waves will be treated. Particular importance will be given to the resolution of problems on the basic topics of the course.
Expected learning outcomes
Mastery of the topics of the program; basic knowledge on classic electromagnetism; ability of analysis and synthesis that enable students to identify the most effective techniques in order to solve the proposed problems.
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
Single session
Responsible
Lesson period
First semester
Course syllabus
1) Electrostatics
Electric charge properties and Coulomb law
Electrostatic induction
Electrostatic force and field
Point-like particles and continuous charge distributions
Field lines -- qualitative description
2) Work and potential of the electrostatic field
Conservativity of the electrostatic force, its potential energy and potential
Field as gradient of the potential
Stokes theorem
Electric dipole
3) Gauss law
Flux of the electrostatic field - Gauss theorem
Discontinuity of the electrostatic field
Maxwell equations (integral and local form) for the electrostatic field in vacuum
Poisson Equation - Laplace Equation
4) Conductors and capacitors
Capacity
Hollow conductor
Capacitors and their capacity
Connected capacitors
Electrostatic energy and pressure
5) Electric current and dc circuits
Current intensity and density
Electric current continuity equation
Stationary current regime
Resistors - Electric resistance, resistivity and conductivity
Ohm laws - Joule effect - Electromotive force
6) Magnetostatics
Lorentz force and magnetic field vector B
Field lines of the magnetic field and Gauss law
Magnetic force and mechanical moments on a conductor with current - Laplace second elementary law - Ampère equivalence principle
Potential energy of a circuit in a magnetic field
7) Magnetic-field sources
Magnetic field due to dc
Biot-Savart law - Laplace first elementary law
Ampère-Laplace law
Ampère circuital law
Magnetic flux
Force among circuits
Maxwell equations (integral and local form) for the magnetic field generated by stationary electric currents in vacuum
8) Time-dependent electric and magnetic fields
Electromagnetic induction - Faraday law - Lenz law
Physical origin of the induced electromotive force
Magnetic field measurements - Felici law
Self-induction - self flux - inductance - self-induced electromotive force
Examples of time-dependent currents: RC circuits, RL circuits
Magnetic energy
Displacement current - Ampère-Maxwell law
Maxwell equations for time-dependent electric and magnetic fields in vacuum (integral and local form)
Electromagnetic energy density
Maxwell equations in terms of potentials
9) Electromagnetic waves
Types of waves, transverse/longitudinal waves
Plane wave - d'Alembert equation
Progressive/regressive waves - Principle of superposition
Plane harmonic wave: amplitude, period, wavelength, frequency, angular frequency
Hints on the Fourier analysis
Wave on an elastic and ideal string: propagation velocity, average power carried by the wave, linear density of mechanical energy, wave intensity
Waves in several dimensions: wave front, plane/spherical/circular harmonic wave, propagation vector, wave-function, average power, amplitude, intensity
From Maxwell equations to the wave equation for E and B fields in vacuum
Plane em wave: properties
Harmonic plane em wave -linear/elliptical/circular polarization
Energy of an em wave - Poynting vector
Intensity carried by an em wave
Continuity equation for the em energy - Poynting theorem
Interaction between em waves and charged matter: energy and linear momentum of an em wave - radiation pressure
10) Hints on Optics
Huygens-Fresnel principle
Interference phenomena: coherent and incoherent sources, interference among two spherical waves
Young's double slit experiment
Electric charge properties and Coulomb law
Electrostatic induction
Electrostatic force and field
Point-like particles and continuous charge distributions
Field lines -- qualitative description
2) Work and potential of the electrostatic field
Conservativity of the electrostatic force, its potential energy and potential
Field as gradient of the potential
Stokes theorem
Electric dipole
3) Gauss law
Flux of the electrostatic field - Gauss theorem
Discontinuity of the electrostatic field
Maxwell equations (integral and local form) for the electrostatic field in vacuum
Poisson Equation - Laplace Equation
4) Conductors and capacitors
Capacity
Hollow conductor
Capacitors and their capacity
Connected capacitors
Electrostatic energy and pressure
5) Electric current and dc circuits
Current intensity and density
Electric current continuity equation
Stationary current regime
Resistors - Electric resistance, resistivity and conductivity
Ohm laws - Joule effect - Electromotive force
6) Magnetostatics
Lorentz force and magnetic field vector B
Field lines of the magnetic field and Gauss law
Magnetic force and mechanical moments on a conductor with current - Laplace second elementary law - Ampère equivalence principle
Potential energy of a circuit in a magnetic field
7) Magnetic-field sources
Magnetic field due to dc
Biot-Savart law - Laplace first elementary law
Ampère-Laplace law
Ampère circuital law
Magnetic flux
Force among circuits
Maxwell equations (integral and local form) for the magnetic field generated by stationary electric currents in vacuum
8) Time-dependent electric and magnetic fields
Electromagnetic induction - Faraday law - Lenz law
Physical origin of the induced electromotive force
Magnetic field measurements - Felici law
Self-induction - self flux - inductance - self-induced electromotive force
Examples of time-dependent currents: RC circuits, RL circuits
Magnetic energy
Displacement current - Ampère-Maxwell law
Maxwell equations for time-dependent electric and magnetic fields in vacuum (integral and local form)
Electromagnetic energy density
Maxwell equations in terms of potentials
9) Electromagnetic waves
Types of waves, transverse/longitudinal waves
Plane wave - d'Alembert equation
Progressive/regressive waves - Principle of superposition
Plane harmonic wave: amplitude, period, wavelength, frequency, angular frequency
Hints on the Fourier analysis
Wave on an elastic and ideal string: propagation velocity, average power carried by the wave, linear density of mechanical energy, wave intensity
Waves in several dimensions: wave front, plane/spherical/circular harmonic wave, propagation vector, wave-function, average power, amplitude, intensity
From Maxwell equations to the wave equation for E and B fields in vacuum
Plane em wave: properties
Harmonic plane em wave -linear/elliptical/circular polarization
Energy of an em wave - Poynting vector
Intensity carried by an em wave
Continuity equation for the em energy - Poynting theorem
Interaction between em waves and charged matter: energy and linear momentum of an em wave - radiation pressure
10) Hints on Optics
Huygens-Fresnel principle
Interference phenomena: coherent and incoherent sources, interference among two spherical waves
Young's double slit experiment
Prerequisites for admission
In order to follow the course, an adequate knowledge of the program of General Physics 1 is required.
Teaching methods
The adopted didactic method is based on lectures with the use of the blackboard, for both theoretical explanations and exercises.
Teaching Resources
P. Mazzoldi, M. Nigro, C. Voci , FISICA, Vol II, EdiSES
Assessment methods and Criteria
The final examination consists of a written test, during which neither books nor notes can be used. The written test is divided into two parts: a) solution of 3 exercises similar to those proposed during the course; b) discussion of a theoretical topic to be chosen from two proposed topics concerning arguments covered during the course. Duration of the written test: 3 hours. The exam is passed if both the grade of part a) and that of part b) is sufficient and the proposed grade is the arithmetic average between the evaluation of part a) and that of part b). Students who wish to improve the proposed mark can request an oral exam which can be taken either during the same exam session or during the following exam session. An insufficient oral test leads to a reduction in the proposed grade. In some situations, the teacher can request an oral exam.
FIS/01 - EXPERIMENTAL PHYSICS
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS
FIS/03 - PHYSICS OF MATTER
FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS
FIS/05 - ASTRONOMY AND ASTROPHYSICS
FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM
FIS/07 - APPLIED PHYSICS
FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS
FIS/03 - PHYSICS OF MATTER
FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS
FIS/05 - ASTRONOMY AND ASTROPHYSICS
FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM
FIS/07 - APPLIED PHYSICS
FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS
Practicals: 48 hours
Lessons: 45 hours
Lessons: 45 hours
Professors:
Pini Davide Enrico, Smirne Andrea
Shifts:
Professor(s)
Reception:
On appointment (also remotely on Zoom, if needed)
5th floor, building LITA room A/5/C4