# GENERAL PHYSICS IIModule MODULE I

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

**Roberto BARBERA**

## Expected Learning Outcomes

The purpose of the course is to provide basic qualitative and quantitative knowledge on the topics of classical electromagnetism included in the "Detailed Course Contents" section, as well as the ability to know how to apply the Scientific Method to solving real and concrete problems.

In particular, and with reference to the so-called __Dublin Descriptors__, the course aims to provide the following knowledge and skills.

**Knowledge and understanding abilities**

Knowledge of the main phenomenological aspects related to electromagnetism, to the structure of matter, and to the interaction between electromagnetic radiation and matter, understanding of their physical implications and their mathematical description.

**Applying knowledge and understanding ability**

Ability to recognize the main physical laws that govern an electromagnetic phenomenon, and to apply them to solve problems and exercises at different levels of complexity and therefore of approximation, with the use of appropriate mathematical tools.

**Ability of making judgements**

Evaluation of the order of magnitude of the variables that describe an electromagnetic phenomenon. Evaluation of the relevance of a physical law (axiom, principle of conservation, universal law, theorem, law in global/integral or local/differential form and its generality, properties of materials, etc.). Ability to be able to evaluate the Physical Model and the corresponding Mathematical Model that best apply to the description of a physical process and therefore to the solution of quantitative problems.

**Communication skills**

Ability to present scientific concepts belonging to Physics but also, and more generally, information, ideas, problems and solutions with properties and inambiguity of language, at different levels and to different, both specialists and non-specialists, audiences.

**Learning skills**

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

## Course Structure

The teaching activity consists of 35 hours of lectures and 12 hours of classroom exercises, both held by the teacher. Further exercises can be either assigned by the teacher for individual study at home or guided by tutors (if available) in "ad hoc" meetings scheduled separately.

If this becomes necessary, the teaching activity may also be carried out in mixed or remote mode and necessary changes may be introduced in order to respect the planned program reported in this document.

## Required Prerequisites

## Attendance of Lessons

## Detailed Course Content

**Introduction.** Fundamental units of the International System. Features of a force. Forces and fields. Symmetry in physics and the vector concept. The electric forces. Electric and magnetic fields. Characteristics of vector fields. The laws of electromagnetism; anticipation of Maxwell's equations and their qualitative analysis. Differential calculus of vector fields (gradient, divergence, rotor, Laplacian). Integral calculus of vectors. Line integrals and circulation concept. Surface integrals and flow concept. Gauss and Stokes theorems. Fields with zero rotor and fields with zero divergence.

**Electrostatics.** Coulomb's law and the superposition principle of the electric field. The electric potential and its relationship with the electric field. The flow of **E**. The law of Gauss and the divergence of **E**. Electric field of a charged sphere. Field lines and equipotential surfaces. Equilibrium in an electrostatic field. Equilibrium in the presence of conductors. Stability of atoms. The electric field of a linear charge. Electric field of a charged sheet and of two plates with opposite charges. Electric field of a charged sphere and a spherical shell. Correctness of dependence 1/r^{2}. The fields of a conductor and the fields within a conductor's cavity. Equations for the electrostatic potential. The electric dipole. The potential of the dipole as a gradient. The dipolar and multipolar approximation of an arbitrary charge distribution. Electric forces in molecular biology: DNA structure and replication. Fields due to charged conductors. Image method. Electric fields in the vicinity of a conducting plane and a conducting sphere. The capacitor. Capacitors in series and in parallel. Dependence of the field from the curvature of a conductor: "tip effect". Methods for determining the electrostatic field. Two-dimensional fields and complex variable functions. Notable examples of electric fields: oscillations in plasmas and colloidal particles in an electrolyte. Electrostatic field of a grid. Electrostatic energy of the charges. Energy of a uniformly charged sphere. The energy of a capacitor and the forces on charged conductors. Energy in the electrostatic field. Energy of a point charge.

**Electrostatic field in the matter.** The dielectric constant. The polarization vector **P**. The polarization charges. The equations of electrostatics in the presence of dielectrics. Fields and forces in the presence of dielectrics. Molecular dipoles. Electronic polarization. Polar molecules and polarization by orientation.

**Magnetostatics.** The magnetic field and the Lorentz force on a moving charge. The cyclotron. The electric current and the conservation of the charge. The magnetic force on a current. The magnetic field of stationary currents, Ampère's law. The magnetic field of a rectilinear wire and a solenoid. Atomic currents. The Earth's magnetic field and the alternation of its sign. Polar lights. The vector potential and the choice of its boundary conditions (magnetostatic gauge). The vector potential due to known currents. Potential vector of a straight wire and a solenoid. Magnetic field of a small coil; magnetic dipole. Law of Biot and Savart. The forces on a current loop and the energy of a magnetic dipole. Mechanical and electrical energy. The energy of constant currents. Comparison between the magnetic field and the vector potential.

**Electrical conduction.** Ohm's law of electrical conduction. Power and Joule effect. Resistors in series and in parallel. Electromotive force (f.e.m.). Charge and discharge a capacitor through a resistor. Displacement current and its evaluation. Maxwell generalization of Ampère's law and effect of time-dependent electric fields. Kirchhoff's laws for electricity networks.

**Variable magnetic fields.** The physics of electromagnetic induction and the Faraday law. The alternating current generator. Scheme of operation of a power plant and entropic effects of the production of electricity through transformation from other forms of energy. Mutual inductance and self-induction. Inductance and magnetic energy. Complex numbers and harmonic motion. Forced oscillator with damping in mechanics and its analogy in electromagnetism. The RLC circuit in series. Electrical resonance and complex impedance. Series and parallel impedances. Resonances in nature.

## Textbook Information

1. R. P. Feynman, R. B. Leighton e M. Sands, *La Fisica di Feynman – Vol. 1 e 2 *(Zanichelli, Bologna);

2. P. Mazzoldi, M. Nigro e C. Voci, *Fisica - Volume II* (EdiSES, Napoli).

## Course Planning

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

1 | Introduzione | Feynman |

2 | Electrostatics | Feynman |

3 | Electrostatic field in the matter | Feynman |

4 | Magnetostatics | Feynman |

5 | Electrical conduction | Feynman, Mazzoldi |

6 | Variable magnetic fields | Feynman, Mazzoldi |

## Learning Assessment

### Learning Assessment Procedures

The final exam consists of a written test followed by an oral exam. The written test, lasting 2 hours, consists of the resolution, justified and clearly commented, (A) of 2 problems related to Module 1 of the course and (B) of 2 problems related to Module 2 of the course. In the case of partial tests, a maximum time of 1 hour is granted to each part (A or B). Students can take any partial test (A or B) in any session compatible with the status of their enrollment (current, outside the prescribed time, etc.). For the resolution of each problem is assigned a score between 0/30 and 7.5/ 30 in relation (1) to the completeness of the description of the Physical and Mathematical Models used for the solution, (2) to the correctness of the mathematical treatment and, of course, (3) to the correctness of the result, both from a numerical and a dimensional point of view.

During the tests it is possible to use any support deemed useful (e.g. books, notes, forms, calculators, etc.) ** except** exercise books (i.e. exercise books with relative solutions) and communication devices (mobile phones, tablets, computers).

Students who obtain a score of less than 15/30 in the written test (7.5 / 30, in the case of partial test) are advised against taking the oral test and are not allowed to take an oral test later than the next written test. However, being discouraged is ** not** equivalent to a formal ban on taking the oral exam, provided that this happens before the next written test.

The overall oral exam consists in the treatment of at least 3 distinct topics of the program, the first of which is chosen by the student. During the oral examination it may be necessary to demonstrate the theorems and important results included in the program with numerical evaluations of the order of magnitude of the physical quantities that are involved in a given phenomenon.

**Information for students with disabilities and/or SLD**

In order to guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and/or dispensatory measures, according to the educational objectives and specific needs.

It is also possible to contact the CInAP (Centro l'Integrazione Attiva e Partecipata - Servizi per le Disabilità e/o DSA) contact-person of the Department, Prof. Patrizia Daniele.

**N.B.**

If this becomes necessary, the learning assessment can also be carried out in mixed or remote mode.

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

Usually, the oral exam begins with the presentation of a topic chosen by the candidate. After that, the exam continues with questions like: "tell me about" ... one of the topics of the program. Some examples are the following:

- "Gauss law"
- "energy of the electrostatic field"
- "electrostatic field in dielectrics"
- "equation of continuiity of the electric charge; in static as well as dynamic conditions"
- "equations of magnetostatics"
- "charge and discharge of an RC circuit; the displacement current"
- "Faraday's law of electromagnetic induction"
- etc.

During the oral examination it may be necessary to demonstrate theorems and important results included in the program with numerical evaluations of the order of magnitude of the physical quantities involved in a given phenomenon.

A collection of exercises, many of which were assigned during the written exam sessions, is available on the course page on the Studium portal (http://studium.unict.it), in the Documents section.