PHYSICS II AND LABORATORY M - Z

The student will acquire the basics for the understanding of Classical Electromagnetism, Geometric and Physical Optics. Moreover, through exercises and problems to be solved in the classroom and at home and the experimental activity in Laboratory, the student will be accustomed to solve concrete problems and to approach experimentally the real world. The student who will have acquired the topics and methodologies of the course, will be able to face and solve problems of various kinds through a logical-scientific approach. In particular, the course proposes the following objectives:

• Knowledge and ability to understand (Knowledge & Understanding): the student will be introduced to the basic knowledge of the laws of classical physics (Electromagnetism and Optics). The student will develop the ability to understand the most important physical phenomena related to the course program.
• Applying Knowledge & Understanding: the student will be initiated to an application in practical fields of acquired knowledge, with continuous examples of applied physics, problem solving and experimental activities in Laboratory for the understanding of the real world.
• Making judgments: the student will be induced to a critical analysis of the level of knowledge acquired, pushing him to a self-assessment of his knowledge and skills, trying to develop an autonomy of judgment on the objectives achieved.
• Communication Skills: the interaction with the teacher and colleagues will be stimulated to increase students' communication skills.

PLEASE NOTE

Informazioni per studenti con disabilità e/o DSA Information for students with disabilities e/o DSA: for equal opportunities and in accordance with the laws in force, the affected students can ask for a personal interview in order to plan possible compensatory or exempting actions on the basis of the educational goals and specific requirements.

The course is composed of 10 CFU for a total amount of 90 hours of activities in Classroom & Laboratory, distributed as following:

a) Lectures in Classroom for a total amount of 6 CFU = 42 hours (1 CFU = 7 hours) that is to say 21 lecturers of 2 hours;

b) Exercises in Classroom (for learning of the methodology of development and solving of Problems and Exercises in Physics 2) for a total amount of 1 CFU = 12 hours that is to say 6 lecturers of 2 hours;

c) Experimental Activities in Laboratory for a total amount of 3 CFU = 36 hours (1 CFU = 12 hours): 27 hours devoted to 9 shifts of 3 hours in Laboratory (one for each experiment of Physics planned in program) and 9 hours devoted to preparation and explanation of the experimental activities.

Contents of the course of MATHEMATICS 1 and MATHEMATICS 2. Contents of the course of PHYSICS1.

• passing and formal registration of the exam in MATHEMATICS 1 (preparatory for PHYSICS 2 and LABORATORY, as reference to "Regolamento Didattico Corso di Laurea in Chimica - Classe L27 - Scienze e Tecnologie Chimiche COORTE 2022-23", approvato dal Senato Accademico nella seduta del 28 giugno 2022);
• passing and formal registration of the exam in MATHEMATICS 1 (preparatory for PHYSICS 2 and LABORATORY, as reference to "Regolamento Didattico Corso di Laurea in Chimica - Classe L27 - Scienze e Tecnologie Chimiche COORTE 2022-23", approvato dal Senato Accademico nella seduta del 28 giugno 2022).

The attendance of this course - both in lectures of Theory & Exercises in Classroom and in experimental activities in Laboratory  - is usually mandatory, since the student has to attend at least 70% of hours spent on work-related activities for each course (please, refer to "Regolamento Didattico Corso di Laurea in Chimica - Classe L27 - Scienze e Tecnologie Chimiche COORTE 2022-23", approvato dal Senato Accademico nella seduta del 28 giugno 2022). 

The attendance will be checked by daily requirement to sign-in, both for each lecture in Classroom and Exercise and Shift of activity in Laboratory.

1. ELECTROSTATICS 

1.1 – Electrical Phenomena: Introduction. Electrostatic forces.  Electrostatic induction. The electric charge. Coulomb's Law. The electrostatic field in the vacuum. Gauss's Law. Calculation of electrostatic fields for discrete and continuous distributions. Motion of a charge in an electrostatic field.

1.2 – The Electric Potential: The electric work. Conservative behavior of the electrostatic field. The electrostatic potential and calculation in main cases. Equipotential surfaces and lines of forces. Potential energy of the electrostatic field and motion of a particle. The II Maxwell's Law. Poisson's and Laplace's equations. Electrostatic field by a dipole.  

1.3 – Conductors and Capacitors: Electrostatic field in conductors. Potential and capacity of conductors. System of more conductors. Capacitors. Electrostatic energy of a charged capacitor. Capacitors with dielectric. Fundamentals of electrostatic in dielectrics.

2. STATIONARY ELECTRICAL CURRENTS

Current intensity. Conservation of the electrical charge. Ohm's Law. Classical model of conduction. Electrical resistance. Generators of f.e.m. Kirchhoff's Laws. Measurements of current, voltage and resistance. Transportation of the electrical energy. Conduction in liquids and gases.

3. STATIONARY MAGNETISM

The magnetism. The experiments of Oersted and Ampere. Lorentz's force and magnetic field. Magnetic field generated by stationary currents. Magnetic forces over circuits crossed by current. Sources of magnetic induction field B and its divergence. Ampere's Law and B's curl. Magnetic filed generated by a moving charge. Motion of charged particle in magnetic fields. Hall's effect. Equivalence between turns and magnetized needles. Magnetic properties of matter. The vector potential.

4. ELECTROMAGNETIC FIELDS

The  Faraday's Law for the electromagnetic induction. Induction due to relative motion. Curl of the electrical field. Mutual induction and self-induction. Inductances in serial and in parallel. Energy density of the magnetic field. Oscillating circuits. Transient phenomena. Maxwell's equations. Electromagnetic fields in matter. Alternating currents. Filters, transformers and measurements with alternating currents. Electromagnetic potentials and delayed potentials. 

5. ELECTROMAGNETIC WAVES

The discovery of the electromagnetic waves. Equation of the electromagnetic waves in vacuum. Planar waves. Electrical and magnetic fields in the planar waves. Energy and pulse of electromagnetic fields. Irradiation by an oscillating charge and dipole radiation. The electromagnetic spectrum.

6. GEOMETRICAL OPTICS

Reflection and refraction of the light. Speed of light in a medium. Refraction index. Cauchy formula. Principle of Huygens-Fresnel. Maximum angle. Total reflection. Chromatic dispersion. Prism. Fresnel coefficients. Brewster's angle. Polarization due to reflection. Polarization due to selective absorption and diffusion. Malus's Law. Double refraction. Construction of images in geometric optics. Spherical and planar mirrors. Focal distance. Magnification. Spherical and planar dioptrics. Dioptric power. Convergent power. Thin lenses. Lens builder equation. Magnification. Optical microscope. Visual enlargement.

7. PHYSICAL OPTICS

The phenomenon of interference. Interference from two slits. Minimum and maximum interference position. Intensity distribution between the fringes. Phase method for calculating intensities. The phenomenon of diffraction. Fraunhofer diffraction from a single rectilinear slit. Diffraction minima position. Minimum resolution angle. Rayleigh criterion. Resolving power of a lens. Linear resolution power of a microscope. Diffraction grating. X diffraction.

8. ELEMENTS of THEORY OF ERRORS 

Uncertainty of a measure. Error sources. Estimate of the uncertainty in the reading of scales. Random errors and systematic errors. Representation of experimental data. Significant figures. Discrepancy between two measures. Graph representation. Verifying relationships with a chart. Relative error or accuracy. Propagation of errors in indirect measures (maximum limit of uncertainty). Propagation of errors in indirect measures (random uncertainties and independent measures).  Statistical analysis of a set of measures: mean and standard deviation. Error on the average. Frequency histograms. Probability distribution of Gauss. Linear best-fit and its uncertainty. Chi-square test. 

9. EXPERIMENTS in LABORATORY

1. Measurement of the elastic constant of a spring. 
2. Measurement of gravity acceleration with the simple pendulum. 
3. Measurement of the viscosity coefficient of glycerine. 
4. Measurement of resistances with the volt-amperometric method. 
5. Measurement of resistances of high value, by means of the discharge of the capacitor. 
6. Measurement of resistances with the Weathstone's bridge or measurement of inductances with a RCL circuit in alternate current.
7. Measurement of the focal distance of a converging lens. 
8. Verification of the Malus law and measurement of concentrations of optically active solutes or Measurement of the focal distance of a diverging lens
9. Measurement of the ratio e/m by magnetic deflection or Measurement of wavelengths through a diffraction grating. 

MAIN REFERENCE TEXTS: 

• "Fisica Generale  - Elettromagnetismo" II edizione - autori: S. Focardi, I.G.Massa, A.Uguzzoni, M. Villa - Casa Editrice Ambrosiana (CEA)
• "Fisica Generale  - Onde e Ottica" II edizione - autori: S. Focardi, I.G.Massa, A.Uguzzoni - Casa Editrice Ambrosiana (CEA)
• "Esercizi di Fisica - Elettromagnetismo" - autori: M.Bruno, M.D'Agostino, R. Santoro - Casa Editrice Ambrosiana (CEA)
• "Introduzione all'analisi degli errori. Lo studio delle incertezze nelle misure fisiche" - autore: J. Taylor - Casa Editrice Zanichelli editore 

OTHER TEXTS:

• "Elementi di Fisica - Elettromagnetismo e Onde" II edizione - autori: P. Mazzoldi, M. Nigro , C. Voci - Casa Editrice EdiSES Università

a)  a written exam, 

b) a practical exam: writing of an essay concerning one of the experimental activities performed during the course;

c) an oral exam. 

Ongoing tests ("Prove in itinere") will NOT be scheduled during this course.

a) The written exam lasts 3 hours and consists of 3 Problem to be solved, concerning respectively topics of Electrostatics,  Stationary Magnetism, Non-Stationary Electromagnetic Fields, Electrical Circuits in direct/alternating current or in transient capacity, Geometric or Physical Optics. For each Problem, a score of 10/30 points will be assigned and the total mark will be evaluated in 30/30. Criteria for the evaluation of the written exam are: accuracy in the preparation of problems, explication of the solving procedures, correct calculation of the numerical results and the corresponding unit of measurements of the physical quantities involved.

b) For the practical exam, on the occasion of the written exam, for each student, one of the experimental activities performed in Laboratory during the semester will be drawn. On the occasion of the oral exam, each student must submit an essay ("Tesina") written on the basis of the experience carried and the experimental data personally taken in Laboratory. Taking into account for the timeliness in consignment, the essay will be judged based on accuracy, completeness, conciseness and properties in correct use of language.

c) The oral exam consists in the discussion of the written exam and practical exam in addition with general questions concerning the program in order to analyze the knowledge developed by the student. These general questions could concern all the topics illustrated during the course. The oral exam must be taken before the date scheduled for the following written examination.

Classic questions asked during the oral examination, concerning fundamental topics (such as Electrostatics, Electromagnetic Fields and Optics), are:

1) write and comment the Coulomb's Law (in vacuum and in matter)  by specifying, for each variable, its meaning and unit of measurement;

2) what is the statement of the Faraday-Neumann's Law? In particular, point out the physical meaning of each physical quantity involved and its unit of measurements;

3) explain the phenomenon of refraction in Geometric Optics and its laws, especially by referring to the experimental activity carried out in Laboratory.