# PHYSICS II

**Academic Year 2023/2024**- Teacher:

**ELISABETTA PALADINO**

## Expected Learning Outcomes

The purpose of the course is to provide basic electromagnetism in vacuum, in the presence of conductors, dielectric and magnetic materials both in stationary conditions and in the presence of time-dependent phenomena, including electromagnetic waves. At the end of the course the student will be able to solve simple electromagnetism problems starting from Maxwell's equations and constitutive relations related to different materials.

With reference to the topics covered in Physics II, the course will promote the following skills:

- **Knowledge and understanding ****abilities****.** Inductive and deductive reasoning skills. Ability to schematize a natural phenomenon in terms of scalar and vector physical quantities. Ability to set a simple problem using appropriate relationships between physical quantities (algebraic, integral or differential) and to solve it with analytical methods.

- **Ability to apply knowledge and understanding.** Ability to apply the knowledge acquired for the description of physical phenomena using rigorously the scientific method. Ability to apply the knowledge acquired to solve simple electromagnetism problems.

-** Making judgments**. Critical reasoning skills. Ability to identify the most appropriate methods to analyze critically, interpret and process the data of a problem.

- **Communication skills.** Ability to present orally, with appropriate language and rigor, a scientific topic, explaining it and illustrating the results.

**- Learning skills**. Ability to learn the scientiﬁc concepts of Physics, necessary to undertake subsequent studies with a high degree of autonomy.

## Course Structure

**Methods of carrying out the teaching**

The teaching is carried out through lectures (for a total of 7 CFU) and exercises (2 CFU) consisting of exercises taken from the reference texts and exams from previous academic years. The exercises will be carried out in cooperative learning mode. The written test can be replaced by two intermediate tests during the course. At the beginning of the course a self-assessment test on the prerequisites required and listed below will be given.

Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

**Previous knowledge**

Text comprehension. Notions of geometry and vector calculus: distinction between scalar and vector quantities, sum of vectors, scalar product and vector product. Knowledge of elementary algebra and trigonometry: solution of first and second algebraic equations degree, trigonometric functions and goniometric formulas. Differential and integral calculus of one-variable functions. Differential equations of the first and second order. Newton's laws and equations of motion. Conservative forces and the principle of conservation of energy mechanics. Translational and rotational dynamics: uniform rectilinear motion and uniform motion accelerated, angular velocity. Force field.

**Lessons attendance**

Attendance to lectures is strongly recommended. Attendance is mandatory to access the ongoing tests (minimum attendance equal to 65%).

**Additional educational material**

The teaching material eventually delivered (in the classroom or via Studium) represents *exclusively *a guide for the student who will still have to study on the recommended Physics texts.

**Learning evaluation**

The exam consists into written (ongoing or regular) and oral tests. Admission to the written test requires booking on the Student Portal platform. This will be possible during a limited time range for each appeal. Admission to the oral exam is subject to passing the written test (ongoing or regular). It is not possible the exam without taking all the tests. At the end of the written test, typically within three days, the test is published on STUDIUM, with the aim of soliciting a process of self evaluation. The results of the written tests are published on STUDIUM.

- **Written tests in progress** There are two written tests during the semester (reserved for students who have followed at least 65% of lessons), ttypically half November and mid-January. Typology: resolution, clearly justified and commented, of two problems, whose level of difficulty is similar to exercises carried out in the classroom. Duration: 60 minutes. Evaluation: up to 7 points for each problem well done. Every in test is passed with a grade of not less than 10. You can take the second ongoing test despite not having passed the first. You are admitted to the oral test only by passing both ongoing tests, booking at the chosen exam on the Student Portal platform. The score associated with the ongoing tests will be the sum of the scores obtained in the two written tests. Students who have passed only one of the two ongoing tests will have the opportunity to sit the written test in an exam session, addressing only the exercises on the topics of the ongoing test not passed. This will be possible only in a single session of the academic year 2020/2021, upon booking for the written test on the Student Portal platform. The score will be the sum of the scores obtained in the passing test and in the remaining part of the written test.

Those who fail the ongoing tests must take the regular written test in one of the exam sessions foreseen by the calendar.

-** Regular written test** The regular written test must be taken in one of the exams foreseen by calendar, upon prior reservation. Typology: termination, justified and commented in a manner clear, of four problems, whose level of difficulty is similar to the exercises carried out in the classroom. Duration: 120 minutes. Evaluation: up to 7 points for each problem well done. Each regular written test is considered passed if a grade of not less than 18/30 is achieved. Students are admitted to the oral exam only by passing the written test.

NOTES: for the written tests (ongoing or regular): i) During the written tests they are admitted only pen, pencil and calculator. Books, forms, mobile phones, consultations between colleagues are NOT allowed. ii) Who, having passed a written test (ongoing or regular), goes to a second written test he loses the result of the first test (even if he decides to withdraw from the second).

- **Oral exam**: The oral exam is taken at a later date than the written one and in any case by same appeal as the written test. Exceptionally, it can be granted to sit the oral exam during the next session, within the same exam session. The oral exam can be repeated one second time, without having to repeat the written test, within the same exam session. The oral exam focuses on four of the topics of the course planning reported in the Syllabus. The first topic is chosen by the student. The evaluation elements of the oral exam will be: relevance of the answers to the questions asked, the quality of the content, the ability to connection with other topics covered by the program, the ability to report examples, the ownership of technical language and the student's overall expressive ability. To take the oral exam it is compulsory to book at the chosen session using the telematic tools provided.

**Dates of the exams**

Check the following web pages: http://portalestudente.unict.it, http://www.dieei.unict.it/corsi/l-8-ele/esami

__Exam booking through the Smart_Edu platform is mandatory__. Non-booked students will not be able to do exams.

The above rules must be understood as useful indications for the student to correct planning and the appropriate preparation for exams, but do not constitute any constraint on the judgment of the examination commission.

Learning assessment may also be carried out on line, should the conditions require it, in this case, the duration of the written test may be subject to change.

**Examples of frequently asked questiona and/or exercises**

Typical exercise first part of the program:

An electric charge is distributed between two concentric spherical surfaces with rays a = 1cm and b = 30cm uniform density r = 31.2 x 10^{-8} in IS units.

1) Derive the electrostatic field in all points of space and the potential by setting the zero of potential to infinity. Calculate the value of the potential at the point r = 35 cm.

2) Calculate how fast an electron initially at rest on the sphere reaches the center of the sphere surface with radius r = 2cm.

Typical exercise second part of the program:

In a square coil with side l = 33 cm, placed on the x-y plane of a Cartesian system, a current flows i = 26 mA. At time t = 0 the half of the coil is subject to the action of a magnetic field B = B **z** with B = 35 mT

1) Calculate the (vectorial) force that must be applied to the loop for it to be at rest in the system reference indicated.

2) Calculate the current induced in the loop when it is in motion at t = 0 at constant speed v = 0.5 x m / s and has resistance R = 5 x 10 3 IS units.

Often asked questions:

Maxwell's equations in integral form;

Maxwell's equations in local form;

Electrostatic field and electric field;

Electrostatic induction;

Drude model;

Ohm's law;

Polarization of dielectric materials;

Magnetic materials magnetization;

Constitutive relationships;

Magnetic field;

Wave equation and electromagnetic wave properties;

Polarization of electromagnetic waves.

## Required Prerequisites

quantities, sum of vectors, scalar product and vector product. Knowledge of elementary algebra and

trigonometry: solution of ﬁrst and second algebraic equations degree, trigonometric functions and

goniometric formulas. Diﬀerential and integral calculus of one-variable functions. Diﬀerential equations of

the ﬁrst and second order. Newton's laws and equations of motion. Conservative forces and the principle

of conservation of energy mechanics. Translational and rotational dynamics: uniform rectilinear motion

and uniform motion accelerated, angular velocity. Force ﬁeld.

## Attendance of Lessons

(minimum attendance equal to 65%).

## Detailed Course Content

**Electrostatic Field**: Electrical charges: phenomenology and Coulomb's law. The principle of superposition. Electrostatic field generated by a set of discrete charges. Force lines. Gauss' law. Electrostatic field produced by continuous distributions of charges. Motion of charges in an electrostatic field. Electrostatic potential: Work of the electric force and the electrostatic potential. Electrostatic potential energy, equipotential surfaces. Tension. Electric dipole. Maxwell's equations for the electrostatic field.

**Conductors and electrical conductance: **Conductors under equilibrium conditions. Conductance of an insulated conductor. Electrostatic screen. Capacitors in series and parallel connections. Energy stored in a capacitor. Dielectric materials: Phenomenology of dielectrics and polarization vector. Qualitative description of the mechanisms of electronic and orientation polarization. Maxwell's equations in dielectric materials. Continuity properties of the electric fields. Energy of the electric field in the presence of dielectric materials. Microscopic model of the electronic polarizability.

**Direct electric current**: Electrical conduction. Electric current. Principle of conservation of charge and continuity equation. Drude model for the conduction and Ohm's law (Joule effect). Resistors in series and in parallel.

**Magnetic field:** Magnetic force: phenomenology. Force lines and Gauss's law for the magnetic field. Lorentz law. Force on current-carrying conductors: elementary laws of Laplace. Ampere's principle of equivalence. Magnetic field produced by currents. Ampere's law. Electrodynamic actions between circuits. Maxwell's equations magnetostatic field. Magnetic media: Phenomenology of magnetic substances and magnetization vector. Maxwell's equations in magnetic media. Continuity properties of the magnetic fields. Energy of the magneticfield in material media. Qualitative discussion of paramagnetism, diamagnetism and ferromagnetism: hysteresis and magnetic shields.

**Time dependent electric and magnetic fields**: Electromagnetic induction, Faraday's Law Lenz. Induced electromotive force. Induction phenomena. Displacement current and Maxwell Ampere's law. Magnetic energy. Maxwell's equations and electromagnetic waves in a vacuum Maxwell equations in vacuum in integral and differential forms. Introduction to electromagnetic waves. D'Alembert equation. Symbolic notation. Plane waves. Harmonic waves. Polarization of electromagnetic waves. Energy density of electromagnetic waves, and the Poynting vector intensity. Maxwell's equations in matter and waves electromagnetic in linear media. Qualitative illustration of the phenomena of absorption and dispersion in dielectric materials and conductors

## Textbook Information

1) P. Mazzoldi, M. Nigro, C. Voci, Fisica volume II Seconda edizione, EdiSES 2000.

2) Fisica 2, D. Halliday, R. Resnick, K. S. Krane, Zanichelli

3) Edward M. Purcell, La Fisica di Berkley 2, Elettricità e Magnetismo, Zanichelli.

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Cariche elettriche; legge di Coulomb; Campo elettrostatico. | Testo 1) Cap. 1 |

2 | Potenziale elettrostatico; energia potenziale associata al campo elettrico. | Testo 1) Cap. 2 |

3 | Legge di Gauss | Testo 1 Cap 3 |

4 | Conduttori; induzione elettrostatica; schermo elettrostatico; capacità di un conduttore isolato. Capacitori, collegamenti in serie e in parallelo. | Testo 1) Cap 4 |

5 | Dielettrici; Polarizzazzione; Equazioni di Maxwell in presenza di dielettrici | Testo 1) Cap 5 |

6 | Trattazione microscopica della polarizzabilità elettronica. | Testo 1) Cap 5 |

7 | Conduzione elettrica; modello di Drude, legge di Ohm, corrente continua. Resistori in serie ed in parallelo. | Testo 1) Cap 6 |

8 | Campo magnetico; forza di Lorentz, leggi elementari di Laplace. | Testo 1) Cap 7 |

9 | Legge di Ampere | Testo 1) Cap 8 |

10 | Mezzi magnetici, magnetizzazione, correnti amperiane. | Testo 1) Cap 9 |

11 | Campi elettrici e magnetici variabili nel tempo: legge di Faraday e legge di Ampere Maxwell | Testo 1) Cap 10 |

12 | Equazioni di Maxwell e onde elettromagnetiche nel vuoto | Testo 1) Cap 13 |

13 | Equazioni di Maxwell nella materia e onde elettromagnetiche nei mezzi lineari | Testo 1) Cap 18 |

## Learning Assessment

### Learning Assessment Procedures

booking on the Student Portal platform. This will be possible during a limited time range for each appeal.

Admission to the oral exam is subject to passing the written test (ongoing or regular). It is not possible

the exam without taking all the tests. At the end of the written test, typically within three days, the test is

published on STUDIUM, with the aim of soliciting a process of self evaluation. The results of the written

tests are published on STUDIUM.

- Written tests in progress There are two written tests during the semester (reserved for students who

have followed at least 65% of lessons), ttypically half November and mid-January. Typology: resolution,

clearly justiﬁed and commented, of two problems, whose level of diﬃculty is similar to exercises carried

out in the classroom. Duration: 60 minutes. Evaluation: up to 7 points for each problem well done. Every

in test is passed with a grade of not less than 10. You can take the second ongoing test despite not

having passed the ﬁrst. You are admitted to the oral test only by passing both ongoing tests, booking at

the chosen exam on the Student Portal platform. The score associated with the ongoing tests will be the

sum of the scores obtained in the two written tests. Students who have passed only one of the two

ongoing tests will have the opportunity to sit the written test in an exam session, addressing only the

exercises on the topics of the ongoing test not passed. This will be possible only in a single session of the

academic year 2020/2021, upon booking for the written test on the Student Portal platform. The score

will be the sum of the scores obtained in the passing test and in the remaining part of the written test.Those who fail the ongoing tests must take the regular written test in one of the exam sessions foreseen

by the calendar.

- Regular written test The regular written test must be taken in one of the exams foreseen by

calendar, upon prior reservation. Typology: termination, justiﬁed and commented in a manner clear, of

four problems, whose level of diﬃculty is similar to the exercises carried out in the classroom. Duration:

120 minutes. Evaluation: up to 7 points for each problem well done. Each regular written test is

considered passed if a grade of not less than 18/30 is achieved. Students are admitted to the oral exam

only by passing the written test.

NOTES: for the written tests (ongoing or regular): i) During the written tests they are admitted only pen,

pencil and calculator. Books, forms, mobile phones, consultations between colleagues are NOT allowed.

ii) Who, having passed a written test (ongoing or regular), goes to a second written test he loses the

result of the ﬁrst test (even if he decides to withdraw from the second).

- Oral exam: The oral exam is taken at a later date than the written one and in any case by same appeal

as the written test. Exceptionally, it can be granted to sit the oral exam during the next session, within

the same exam session. The oral exam can be repeated one second time, without having to repeat the

written test, within the same exam session. The oral exam focuses on four of the topics of the course

planning reported in the Syllabus. The ﬁrst topic is chosen by the student. The evaluation elements of the

oral exam will be: relevance of the answers to the questions asked, the quality of the content, the ability

to connection with other topics covered by the program, the ability to report examples, the ownership of

technical language and the student's overall expressive ability. To take the oral exam it is compulsory to

book at the chosen session using the telematic tools provided.

Dates of the exams

Check the following web pages: http://portalestudente.unict.it,

http://www.dieei.unict.it/corsi/l-8-ele/esami

Exam booking through the Smart_Edu platform is mandatory. Non-booked students will not be able to

do exams.

The above rules must be understood as useful indications for the student to correct planning and the

appropriate preparation for exams, but do not constitute any constraint on the judgment of the

examination commission.

Learning assessment may also be carried out on line, should the conditions require it, in this case, the

duration of the written test may be subject to change.

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata - Servizi per le Disabilità e/o i DSA) referring teacher within their department.

### Examples of frequently asked questions and / or exercises

An electric charge is distributed between two concentric spherical surfaces with rays a = 1cm and b = 30cm uniform density r = 31.2 x 10 -8 in IS units.

1) Derive the electrostatic ﬁeld in all points of space and the potential by setting the zero of potential to inﬁnity. Calculate the value of the potential at the point r = 35 cm.2) Calculate how fast an electron initially at rest on the sphere reaches the center of the sphere surface with radius r = 2cm.

Typical exercise second part of the program:

In a square coil with side l = 33 cm, placed on the x-y plane of a Cartesian system, a current ﬂows i = 26 mA. At time t = 0 the half of the coil is subject to the action of a magnetic ﬁeld B = B z with B = 35 mT

reference indicated.

2) Calculate the current induced in the loop when it is in motion at t = 0 at constant speed v = 0.5 x m / s and has resistance R = 5 x 10 3 IS units.

Often asked questions:

Maxwell's equations in integral form;Maxwell's equations in local form;

Electrostatic ﬁeld and electric ﬁeld;

Electrostatic induction;

Drude model;

Ohm's law;

Polarization of dielectric materials;

Magnetic materials magnetization;

Constitutive relationships;

Magnetic ﬁeld;

Wave equation and electromagnetic wave properties;

Polarization of electromagnetic waves.

**VERSIONE IN ITALIANO**