19704 - General Physics B

Learning outcomes

At the end of the course the student has assimilated and is able to apply the knowledge on the basic concepts of the General Physics in the language of the Mathematical Analysis, of the Integral and Vector Calculus; he has assimilated and is able to apply the technical-scientific methodology needed in order to face in quantitative terms the physics problems.

Course contents

1. Electrostatics. The 4 fundamental forces of the nature: gravitational interaction, weak interaction, electromagnetic interaction, strong interactions. Matter particles: quark and leptons. Interaction particles: bosons. Triboelectricity, lightning and thunderbolts. The principle of superposition. Continuous distributions of electric charge. The electric field. Electric field representation by means of field lines. The flux of the electric field. The Gauss law for the electric field. Divergence of a vector field. The Gauss theorem (or divergence theorem). Local form of the Gauss law for the electric field. Electrostatic potential.
2. Conductor electrostatics. Dielectrics and conducting media. Charge distribution, electric field and potential inside conductors. Electrostatic induction. Electric field on conductor surface. Electric field in a cavity inside a conductor, electrostatic screen, Faraday cage. Complete induction. The meaning of grounding. Potential of a charged conducting sphere. The power of points. Conductor capacity. Capacitors and their capacity. Capacitors linked in series and in parallel.
3. The general problem of the electrostatics. Electrostatic energy of a point charge system. Electric dipole. Electrostatic energy of a charged capacitor. Electrostatic energy density associated with an electric field. Localization of the electrostatic energy. Locality of the energy conservation principle. Poisson and Laplace's equations. The general problem of the electrostatics.
4. Electric current. Electric current, Drude-Lorentz model, drift velocity and thermal velocity of the conduction electrons.current strength and current density. Ohm's law in the integral and local form, resistance, conductance, resistivity and conductivity. Resistors. Resistors linked in series and in parallel. Dissipated power, Joule's law. Superconductors. Electric generators. Non-electrostatic and non-conservative characteristic of the forces that move the electric charges in an electric generator. The Van der Graaf's generator. Direct-current circuits. Long-distance power lines: use of high voltages to reduce the power dissipation. Transient in a RC-circuit: charge and discharge of a capacitor.
5. Magnetic force. The interaction between two charged particles in uniform motion. Ampère-Biot-Savart law. Magnetic force and its characteristics. Continuous distribution of charge in motion. Local conservation of the electric charge, continuity equation in integral and local form. The magnetic field, Lorentz's force, magnetic force on a continuous distribution of charge in motion due to a magnetic field, magnetic field generated by a continuous distribution of charge in motion. Electric wires, first and second Laplace's formulae, Biot-Savart law, magnetic field generated by a circular loop and by a solenoid. Force between two rectilinear electrical wires. Definition of the Ampère unit.
6. The equations of the magnetic field. Tubes of flux. Flux of the magnetic field. Gauss law for the magnetic field in integral and local form. Absence of the magnetic charge. Circulation of the magnetic field. Ampère-Maxwell's law in integral and local form. Maxwell displacement current. Ampère-Maxwell's law and conservation of the electric charge. Calculations of magnetic fields using the Ampère-Maxwell's law: indefinite rectilinear electric wire, solenoid.
7. Electromagnetic induction. Null flux non-conservative electric fields. Circulation of the electric field. Faraday-Lenz's law in integral and local form. Induced electric field, electromotive force and induced current. The Maxwell's equations.
8. Electric circuits. Self inductance. Inductance of a solenoid. Energy accumulated in a solenoid covered by a stationary electric current. Energy density associated to a magnetic field. Mutual inductance. Transformers. Mean value and root-mean-square value (effective value). Alternate current. Galileo Ferrari's formula. Circuit elements: resistors, capacitors, inductors and electromotive force generators. Electric networks, Kirchhoff's laws and Maxwell's rule. Transient in a RL-circuit. Extracurrents. Oscillating RLC-series circuit: analogy with the mechanical damped oscillator. The complex formalism. Stationary state of a RLC-series circuits submitted to an alternate electromotive force. Impedance, resistance, reactance, admittance, conductance and susceptance.
9. Electromagnetic waves. Density of the energy flux, Poynting vector. Energy conservation and Poynting theorem. Electromagnetic waves, d'Alambert's equation. Solutions of the d'Alambert's equation: plain progressive and regressive waves, spherical converging and diverging waves. Transversality of the electromagnetic waves. Relation between the electric and the magnetic field in an electromagnetic wave. Linear, circular and elliptic polarization. Right-handed and left-handed polarization. Non-polarized and partially polarized electromagnetic waves. Method of polarization of the electromagnetic waves: selective emission, selective absorption, single scattering and reflection. Perfect polarizer. Malus's law. Brewster's angle. Birefringent plates. Application: anti-glare glasses, liquid crystals.
10. Thermodynamic Systems and Molecular Motion. The relationship between microscopic mechanical quantities and macroscopic thermodynamic quantities. Adiabatic and diathermic walls. Thermal contact. Thermal equilibrium between two thermodynamic systems. Thermodynamic equilibrium. Thermometers: thermometric substance, property, and function. Zeroth Law of Thermodynamics. Calibration of thermometers. Fixed points: normal melting point, normal boiling point, and triple point. The ideal gas thermometer. Units of temperature measurement. Thermodynamic transformations.
11. Equation of State for Ideal Gases. Mole and Avogadro’s number. Atomic mass and molecular mass: the atomic mass unit. Quasi-static transformations. Clapeyron diagram. Quasi-static isothermal transformations of a gas. Quasi-static isochoric heating and cooling of a gas. Quasi-static isobaric transformations of a gas. Van der Waals equation: molar covolume and cohesion pressure. Isothermal transformations of real fluids, critical temperature, saturated vapor pressure, and phase transitions (overview).
12. First Law of Thermodynamics. Work in quasi-static transformations of a fluid. Heat. Heat capacity, molar heat, and specific heat. Latent heats. Extension of the principle of energy conservation; internal energy of a thermodynamic system. Free expansion and spontaneous compression.
    Kinetic-molecular theories. Equipartition of energy. Quasi-static adiabatic transformations: Poisson's equations. Enthalpy and technical work (overview).
13. Second Law of Thermodynamics. Heat engines. Efficiency of a heat engine. Refrigerating systems. Second Law of Thermodynamics: Kelvin–Planck and Clausius statements and their equivalence. Impossibility of perpetual motion of the first and second kind. Reversible and irreversible transformations. Carnot engine. Carnot’s theorem. Absolute thermodynamic temperature. Clausius’ theorem. Entropy. The law of entropy increase. Examples of entropy variation calculations in reversible and irreversible processes. Free expansion and spontaneous compression of a gas: Poincaré recurrence time. Internal energy equation and Enthalpy equation (overview). Helmholtz and Gibbs thermodynamic potentials and their properties (overview).

Readings/Bibliography

Bibliography (Thermodynamics)

• Feynmann, Leighton, Sands, The Feynmann Lectures on Physics, vol I, Addison-Wesley.
• C. Mencuccini e V. Silvestrini, Fisica, Meccanica e Termodinamica, Casa Editrice Ambrosiana, Milano.
• Focardi, Massa, Uguzzoni, Fisica Generale, Meccanica e Termodinamica, Casa Editrice Ambrosiana, Milano.

Bibliography (Electromagnetism)

• Feynmann, Leighton, Sands, The Feynmann Lectures on Physics, vol II, Addison-Wesley.
Focardi, Massa, Uguzzoni, Fisica Generale, Elettromagnetismo, Casa Editrice Ambrosiana, Milano.
• Focardi, Massa, Uguzzoni, Fisica Generale, Onde e Ottica, Casa Editrice Ambrosiana, Milano.
• Amaldi, Bizzarri, Pizzella, Fisica Generale, elettromagnetismo, relatività, ottica, Zanichelli, Bologna.

Additional material

• Copies of the slides and the digital boards presented during the classes will be made available on Virtuale
• Question and exercises for the assessment will be made available on Virtuale

Teaching methods

During the frontal lessons blackboard/tablet is used and slides or multimedia are shown by means of a projector. The proposed exercise sessions require the use of the pocket calculator.

To communicate with students, the course Virtuale's Annunci  page is widely used as well as Virtuale's Forums.

Assessment methods

The assessment method for the Integrated Course in General Physics (C.I.) consists of two separate written exams, which may be taken on different days (within the same academic year) or on the same day: one for the General Physics A module and one for the General Physics B module.

The exam for each of the two modules (General Physics A and General Physics B) is written and administered via the Esami OnLine (EOL) platform. 

Each test comprises multiple-choice questions and exercises related to the content covered during lectures:

• All multiple-choice questions have only one correct answer, which awards a positive score (+1). Incorrect answers incur a negative penalty of (−1/number_of_incorrect_choices).
• In the EOL-based exercises, students must provide the required numerical values, expressed in the specified units of measurement. Answers must demonstrate familiarity with the rules of dimensional analysis and the ability to perform numerical calculations with appropriate approximation. Assessment is based on the accuracy of the reported values.
  
  In addition to questions and EOL-based exercises, students must solve one original problem, to be written in full on a separate paper sheet. Both the final result and the reasoning used in solving the problem will be evaluated.

A minimum score of 18 is required to pass each module exam.

The maximum score for the written exam is 29. Up to three additional points can be earned by completing the "exam preparation assignments", which will be made available on the course’s Virtuale page at the end of each lecture block. Completing each of the three assignments grants one extra point.

• These preparation assignments (which draw from the same database of exercises as the exam) may be completed online at any time before the exam date and can be repeated as often as needed until passed.

Honors ("lode") may be awarded for a module if a student demonstrates outstanding performance by achieving the maximum score in both the exam and all three preparation assignments.

The final grade for the Integrated Course in General Physics (C.I.) is considered passing if both module exams (General Physics A and B) are passed.

• The final grade is then the average of the two module scores.
• Honors in the final grade will be awarded if both module exams receive honors.

The teaching staff reserves the right to further assess students’ preparation through an oral interview, if deemed necessary.

Additional details regarding the exam structure, organization, and grading criteria will be provided on the course’s Virtuale page.

Students with Specific Learning Disorders (SLD) or other special needs are strongly advised to contact the appropriate University Office at least 15 days in advance. This office will propose any necessary accommodations, which must be approved by the teaching staff and evaluated in light of the course’s learning objectives.

Teaching tools

Blackboard, tablet, projector, laptop.

Office hours

See the website of Carlo Battilana

See the website of Matteo Franchini