# FUNDAMENTAL OF PHYSICS 2

6 credits during the 1st year of 10375 CHEMICAL AND PROCESSES ENGINEERING (L-9) GENOVA

OVERVIEW

The course is designed for first-year students of Electrical Engineering and Chemical Engineering. The topics relate to the classical electromagnetism from the electric field to Faraday's law, including the RL circuit. Excluded from the course are oscillating circuits, AC circuits and electromagnetic waves.

## AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

The specific training objective is to provide the student with the ability to solve elementary but concrete problems. This implies that the student must know how to distinguish between fundamental concepts (electric and magnetic fields and forces, works, Gauss's laws, Ampere's, Faraday's, ...) and more specific issues (motion of charges in electromagnetic fields, cylindrical condensers, .. .) demanding a thorough understanding of fundamental concepts.

Teaching methods

If permitted by the measures aimed at containing the pandemic Covid-19, I will make lectures on the blackboard, otherwise via streaming on Teams. If possible, I will offer the streaming via Teams also in case of traditional lectures.

SYLLABUS/CONTENT

Introduction to the course, recalls (vectors, significant digits, units).

Electrical phenomena. Coulomb's law. Exercise: comparison between electrostatic and gravitational force. Superposition principle.

The electrostatic field for point charge, discrete distribution, continuous distribution. Exercise: electrostatic field of a charged ring. Exercise: electrostatic field of a charged disk, infinite R limit. Electrostatic field of two charged infinite planes. Field lines.

The work of the electrostatic field: potential and potential energy for a point charge, a discrete system and a continuous system of charges. Exercise: potential and potential energy of a system of 3 point charges. Electric field as a gradient of potential. Exercises: potential of a uniform field, undefined parallel charged planes; potential of a charged ring. Potential of the charged disc.

Motion of a charge in an electric field, conservation of energy. Exercises: electron in a uniform field; classic model of the Bohr atom; electrostatic separator.

The electric dipole. V and E. Forces on a dipole immersed in E (uniform). Torque and energy.

Construction of the concept of flow of a vector field with the analogy of fluid physics. Flow of the electrostatic field. Gauss theorem and proof only in the case of spherical surface and point-like charge. Exercises: E and V of a superficial spherical charge distribution; E and V of a uniformly charged sphere; E and V of a uniformly charged cylinder; E and V of an infinite charged plane.

Conductors in equilibrium electrostatic, conductors with cavities, charge inside cavities, electrostatic induction.

Capacitors. Spherical, flat, cylindrical capacitors. Electrostatic energy of a capacitor, energy density. Capacitors in series and in parallel. Dipole oscillating in E.

Classic model for electrical conduction, drift velocity, current density, current. Ohm's law, Joule effect, series and parallel resistors, electromotive force. Kirchhoff's laws, charge and discharge of a condenser.

The magnetic field: empirical observations. Lorentz's force. Particle moving in uniform B, angular velocity. Examples: mass spectrometer; speed selector; cyclotron.

Force on a current-carrying conductor and immersed in B; mechanical torque on a coil.

Magnetic field produced by a current (Laplace's law) and by a moving charge. Applications: rectilinear wire (Biot-Savart law); circular coil. Applications: rectilinear solenoid. Forces between wires covered by current.

Ampère's theorem and demonstration in the case of rectilinear thread. Applications: wire field, rectilinear solenoid and toroidal solenoid.

The flow of B. Solenoidal fields.

Law of Faraday-Neumann-Lenz. Continuous and alternate current generator. Law of Felici.

Self-induction. Inductance of a solenoid, RL circuit, closing overcurrent. Magnetic energy. Mutual induction (outline).

Displacement current. Maxwell equations

RECOMMENDED READING/BIBLIOGRAPHY

P. Mazzoldi, M. Nigro, C. Voci, "Elementi di fisica - elettromagnetismo", EdiSES

D. Halliday, R.Resnick, J.Walker, “Fondamenti di Fisica” II ; Ed. CEA

## TEACHERS AND EXAM BOARD

**Ricevimento:** Every day, by appointment via email.

## LESSONS

Teaching methods

If permitted by the measures aimed at containing the pandemic Covid-19, I will make lectures on the blackboard, otherwise via streaming on Teams. If possible, I will offer the streaming via Teams also in case of traditional lectures.

LESSONS START

In the second semester, usually at the end of February

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

## EXAMS

Exam description

The exam consistes in a written test and an oral examination

Written exam: the written test consists in the solution of four problems: two problems of Mechanics and two of Electromagnetism; duration of the test 4 hours; it is not allowed to consult books or notes, but only the form used during the year (downloadable from the AulaWeb page)

The student must choose whether to deliver:

- within 2 hours the solution of the test of Mechanics or Electromagnetism, or

- within four hours the solution of both tests

The results of the writings for the individual parts are considered valid for one year (up to the same session of the following academic year).

Oral exam:

1. students who obtain in the two partial tests during the course, or at the exam sessions, an average of 15/30, with a minimum of 12/30 in each test are admitted to the oral exam.

2. The oral examination consists of an interview concerning the mechanical part and the electromagnetism part. Should one of the two interviews be considered insufficient, the oral exam will be considered as globally invalid and the student will have to repeat it in full (the written tests will still be held valid).

Assessment methods

The written exam will evaluate the ability to: i) interpret the text of the proposed exercise and outline the problem; ii) identify the physical laws involved and the related equations to be applied; iii) quantitatively resolve the exercise; iv) evaluate the reasonableness of the numerical result obtained.

In order to evaluate the written test, the following parameters will be taken into account: the correct setting of the exercise, the correctness of the literal solution obtained, the congruence of the numerical solution obtained.

The oral exam will allow to ascertain the ability to: i) introduce the requested topic with language properties; ii) describe simple applications of the physical laws under consideration.

In order to evaluate the oral exam, the following parameters will be taken into account: the level of understanding of the topic, the quality of the presentation, the correct use of the specialist vocabulary, the capacity for critical reasoning.