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General Physics 2

A.Y. 2020/2021

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
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

Teaching methods - Lectures and exercises will be held using the Zoom or Microsoft Teams platform, mainly in synchronous mode, following the official timetable of the degree course in Mathematics.

Program and reference material - will not change.

Learning assessment procedures and evaluation criteria - The final exam will be carried out using the Zoom or Microsoft Teams platform, following the methods illustrated on the Ariel portal and with the same structure as the face-to-face tests. The assessment criteria will be the same as those indicated for the non-emergency situations.

Student reception meetings will be organized with the Zoom or Microsoft Teams platform.

Program and reference material - will not change.

Learning assessment procedures and evaluation criteria - The final exam will be carried out using the Zoom or Microsoft Teams platform, following the methods illustrated on the Ariel portal and with the same structure as the face-to-face tests. The assessment criteria will be the same as those indicated for the non-emergency situations.

Student reception meetings will be organized with the Zoom or Microsoft Teams platform.

**Course syllabus**

Electrostatics

Electric charge properties and Coulomb law

Electrostatic induction

Electrostatic force, field and potential

Point-like particles and charge continuum distributions

Electrostatic energy of a charge system

Flux of the electrostatic field - Gauss theorem

Maxwell equations (integral and local form) for the electrostatic field in vacuum

Poisson Equation - Laplace Equation

Conductors and capacitors - Capacity - Electrostatic energy

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

Magnetostatics

Lorentz force and magnetic field vector B

Magnetic force and mechanical moments on a conductor with current - Laplace second elementary law - Ampère equivalence principle

Magnetic field due to dc: Biot-Savart law - Laplace first elementary law - Ampère-Laplace law

Ampère circuital law

Magnetic flux

Maxwell equations (integral and local form) for the magnetic field generated by stationary electric currents in vacuum

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

Electric oscillations: ideal LC circuits

Displacement current - Ampère-Maxwell law

Maxwell equations for time-dependent electric and magnetic fields in vacuum (integral and local form)

Electromagnetic energy density

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/cylindrical harmonic wave, propagation vector, wave-function, average power, amplitude, intensity

Electromagnetic waves (em waves)

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

Electric charge properties and Coulomb law

Electrostatic induction

Electrostatic force, field and potential

Point-like particles and charge continuum distributions

Electrostatic energy of a charge system

Flux of the electrostatic field - Gauss theorem

Maxwell equations (integral and local form) for the electrostatic field in vacuum

Poisson Equation - Laplace Equation

Conductors and capacitors - Capacity - Electrostatic energy

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

Magnetostatics

Lorentz force and magnetic field vector B

Magnetic force and mechanical moments on a conductor with current - Laplace second elementary law - Ampère equivalence principle

Magnetic field due to dc: Biot-Savart law - Laplace first elementary law - Ampère-Laplace law

Ampère circuital law

Magnetic flux

Maxwell equations (integral and local form) for the magnetic field generated by stationary electric currents in vacuum

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

Electric oscillations: ideal LC circuits

Displacement current - Ampère-Maxwell law

Maxwell equations for time-dependent electric and magnetic fields in vacuum (integral and local form)

Electromagnetic energy density

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/cylindrical harmonic wave, propagation vector, wave-function, average power, amplitude, intensity

Electromagnetic waves (em waves)

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

**Prerequisites for admission**

In order to easily follow the course, an adequate knowledge of the program of General Physics 1 is required.

**Teaching methods**

Traditional

**Teaching Resources**

P. Mazzoldi, M. Nigro, C. Voci , FISICA, Vol II, EdiSES

C. Mencuccini, V. Silvestrini, FISICA II, Liguori Editore

C. Mencuccini, V. Silvestrini, FISICA II, Liguori Editore

**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 (maximum score 30/30); b) discussion of a theoretical topic to be chosen from two proposed topics concerning arguments covered during the course (maximum score 28/30). Duration of the written test: 3 hours. The exam is passed if both the grade of part a) and that of part b) is ≥ 18/30 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 - University credits: 0

FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 0

FIS/03 - PHYSICS OF MATTER - University credits: 0

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0

FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 0

FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS - University credits: 0

FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 0

FIS/03 - PHYSICS OF MATTER - University credits: 0

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0

FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 0

FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS - University credits: 0

Practicals: 48 hours

Lessons: 45 hours

Lessons: 45 hours

Professors:
Cavinato Michela, Pini Davide Enrico

Educational website(s)

Professor(s)