FISICA GENERALE II 1

Module EXERCISES

The General Physics II course aims to study the phenomena and laws of electromagnetism in a vacuum, in the presence of conductors, semiconductors, and dielectric and magnetic materials. The first part of the course provides basic knowledge of electrical and magnetic phenomena in steady-state conditions, while the second part covers the general cases of time-varying fields, summarized in Maxwell's equations, including phenomena related to the propagation of electromagnetic waves in a vacuum and in material media. The final part of the course introduces the key concepts of special relativity, emphasizing its close connection to electromagnetism, and discusses the main phenomena affecting modern physics (photoelectric effect, blackbody radiation, Compton effect) in order to highlight the limitations of classical theory and introduce the first foundations of quantum theory.

Upon completion of the course, students will have acquired inductive and deductive reasoning skills and will be able to schematize problems, particularly those related to electromagnetism, in terms of the appropriate physical quantities and correct laws. In general, students will be able to critically approach the topics studied, formulate a problem, and solve it using analytical methods, carefully addressing both mathematical and physical aspects. Specifically, students will be able to apply the scientific method to the study of electromagnetism phenomena and will be able to critically evaluate similarities and differences between physical systems and the appropriate methodologies.

The course includes classroom lectures (11 credits) and two modules of exercises (3 credits each), which take place concurrently. Overall, the course aims to provide students with the knowledge and methodological tools to competently address problems in general physics, particularly those related to electromagnetism.

More specifically, the learning outcomes in reference to the Dublin Descriptors:

1. Knowledge and Understanding:

- Provide a methodical approach to addressing various problems related to electromagnetism in vacuum and in materials covered during the course.

- Provide concrete examples and connections to solution methods used in other areas of physics.

- Further develop problem-solving skills in general physics problems.

2. Applying Knowledge and Understanding:

- Inductive and deductive reasoning skills.

- Rigorous application of acquired knowledge to describe physical phenomena using the scientific method.

- Use of the laws of electromagnetism to practically solve even complex problems.

3. Making Judgments:

- Ability to formulate a problem using appropriate mathematical relationships (algebraic equations, differential equations, integrals) between physical quantities and to solve these relationships using analytical or numerical methods.

- Perform calculations on complex problems to deduce new results from the laws of electromagnetism (Maxwell's equations).

- Interpret the results obtained from solved problems and verify their validity.

4. Communication Skills:

- Clearly and effectively present fundamental concepts and solutions to solved problems through oral and written reports.

- Actively participate in solving problems addressed in class and in the discussion of possible related topics.

5. Learning Ability:

- Demonstrate the ability to reason independently in order to correctly solve problems posed in class.

- Acquire new knowledge and further explore the topics covered during the course.

- Be able to connect the general concepts of electromagnetism and relativity to recent developments in theoretical and experimental physics.

3 credits for exercises in the first and second semesters

Information for students with disabilities and/or learning disabilities (LD).

To ensure equal opportunities and in compliance with applicable laws, interested students may request a personal interview to plan any compensatory and/or extenuating measures, based on their educational objectives and specific needs. Students may also contact the CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or Learning Disabilities) contact teacher in the Department of Physics.

1. Electrostatics in a vacuum.

Origin of electric charges, structure of atoms (classical description) - Electric actions - Coulomb's law - Electric field - Electrostatic field generated by systems of charges with fixed spatial distribution - Electric dipole - Gauss's theorem - Maxwell's first equation - Divergence theorem - Electric potential - Mechanical actions on electric dipoles in an external electric field - Curvature of a vector field

2. Systems of conductors and the electrostatic field.

Review of Charge Distribution in Conductors (Electron Energy Bands) - Electrostatic Field and Charge Distributions in Conductors - Capacitance - Capacitors - Electrostatic Field Energy - The General Problem of Electrostatics in a Vacuum - Poisson Equation - Image Charge Method - One-Dimensional Laplace Equation

3. Electrostatics in the Presence of Dielectrics

Structure and Charge Distribution in Dielectrics (Electron Energy Bands) - Dielectric Constant - Microscopic Interpretation - Polarization by Deformation and Orientation - The Electric Polarization Vector P - Equations of Electrostatics in the Presence of Dielectrics - The General Problem of Electrostatics in the Presence of Dielectrics and Boundary Conditions for the Vector E and D - Electrostatic Energy in the Presence of Dielectrics - Electrostatic Machines

4. Steady Electric Current in Conductors

Structure and Charge Distribution in Conductors (Electron Energy Bands) - Electric Current - Current Density and Continuity Equation – Kirchhoff's Laws – Electrical Resistance and Ohm's Laws – Dissipative Phenomena in Current-Carrying Conductors – Electromotive Force and Electric Generators – Some Examples of Electric Generators – Electrical Resistance of Ohmic Conducting Structures – DC Circuits – Charges on Current-Carrying Conductors – Electrical Conduction in Liquids – Electrical Conduction in Gases – Superconductors (Notes) – Notes on Methods for Measuring Current, Potential Differences, and Resistance – Quasi-Stationary Current-Carrying Circuits

5. Semiconductors

Structure and Charge Distribution in Semiconductors (Electron Energy Bands) – Intrinsic and Doped Semiconductors – N-Type and P-Type Doping – Law of Mass Action – Electrical Resistivity in Semiconductors – P/N Junction and Its Polarization – Diodes – Photovoltaic Cells

6. Stationary Magnetic Phenomena in a Vacuum

Phenomenology of Magnetic Fields (Permanent Magnets, Magnetic Poles) (and flux lines) - Lorentz force and magnetic flux density vector - Mechanical actions on circuits carrying steady currents in an external magnetic field - Field B0¬ generated by steady currents in a vacuum - Properties of the magnetic flux density vector B0¬ in the steady case - Vector potential - Interactions between circuits carrying steady currents - Hall effect

7. Magnetism in matter

General introductory considerations - General information on the atomic aspects of magnetism - Magnetic polarization and its relationship with microscopic currents - Fundamental equations of magnetostatics in the presence of matter and connection conditions for B¬ and H¬ - Macroscopic properties of dia-, para-, and ferromagnetic materials - Microscopic interpretation of the magnetization phenomena of matter - Relationship between local microscopic fields and macroscopic fields - Larmor precession - Polarization by orientation and Langevin function - Microscopic interpretation of diamagnetism - Microscopic interpretation of paramagnetism - Microscopic interpretation of ferromagnetism - Circuits Magnetic fields, electromagnets, and permanent magnets - Magnetic circuits - Electromagnets - Permanent magnets

8. Time-varying electric and magnetic fields

Time-varying electric and magnetic fields - Electromagnetic induction. The Faraday-Neumann Law - Physical Interpretation of the Phenomenon of Electromagnetic Induction - Sheared Flux: Circuit Configuration Varying in a Magnetic Induction Field B Constant Over Time - Variation of the Linked Flux Due to the Motion of the Field Sources - Variation of the Linked Flux Due to Variations in the Supply Current of the Source Circuits - Local Form of the Faraday-Neumann Law and Expression of Maxwell's Third Equation in the Non-Stationary Case 340 4. Self-Induction Phenomenon and Self-Induction Coefficient - Mutual Induction - Energy Analysis of an RL Circuit - Magnetic Energy and Mechanical Actions - Reference to Electric Energy and Mechanical Actions - Magnetic Energy in the Case of Coupled Circuits - Magnetic Energy and Forces on Circuits - Electric Generators and Electric Motors - Maxwell's Fourth Equation in the Non-Stationary Case

9. Alternating Currents

Alternating Currents - Introductory Considerations - General Considerations on Second-Order Linear Differential Equations - Analysis of the LC Circuit - Analysis of the Series and Parallel RLC Circuit - Alternating Quantities - Fourier Series Expansion of Periodic Quantities - The Symbolic Method - The Phenomenon of Resonance - Power Absorbed by AC Circuits - Static Transformer - Instruments for Measuring Alternating Electrical Quantities

10. Electromagnetic Waves

Electromagnetic Waves - Introductory Considerations - Electromagnetic Wave Equation - Plane Electromagnetic Waves - Spherical Waves - Electromagnetic Waves in Dielectrics. Dependence of the Refractive Index on Wave Frequency - Electromagnetic Waves in Conductors - Spectrum of Electromagnetic Waves - Conservation of Energy and the Poynting Vector - Momentum of an Electromagnetic Wave - Polarization of a Wave

11. Classical Phenomena of Interaction between Radiation and Matter

Conditions for Fields Passing from One Material Medium to Another - Reflection and Refraction of Electromagnetic Waves - Characteristics of Reflected and Refracted Waves. Snell's Law - Dynamic Characteristics of Reflection and Refraction - Dispersion of Light. Spectral analysis and refractive index measurement - Reflection on polished metal surfaces - Natural light and polarized radiation - Group velocity - Huygens-Fresnel principle and Kirchhoff's theorem - Interference - Diffraction - Fraunhofer diffraction from a single straight slit - Fraunhofer diffraction from a circular hole - Interference and diffraction from a double slit - Diffraction gratings - Light guides and optical fibers - Coaxial cables - Waveguides

12. Geometric optics

Approximations of geometric optics. Light rays - General definitions - Reflection: mirrors - Refraction: diopter - Centered diopter systems - Lenses - Properties of some optical devices

13. Photons and matter

Classical theory of blackbody radiation - Planck's law for the blackbody spectrum - Photoelectric effect - Compton effect - Bohr atom - Particle-wave duality. Introduction to the concepts of quantum mechanics - Wave function - Uncertainty principle - Schrödinger equation - Lasers - Conduction in solids - Electrons in atoms - Electrons in solids

14. Special relativity

Postulates of the theory of special relativity - Relativity of simultaneity - Michelson-Morley experiment - Lorentz transformations - Length contraction and time dilation - Relativistic Doppler effect - Lorentz transformations for electric and magnetic fields.

1) C. Mencuccini, V. Silvestrini "Elettromagnetismo e Ottica", Zanichelli

2) P. Mazzoldi - M. Nigro - C. Voci, Fisica, vol. II, EdiSES

3) D.J. Griffiths, Introduction to electrodynamics (IV ed.), Cambridge University Press

Altri testi di consultazione utili per lo studio della materia:

4) E.M. Purcell, La Fisica di Berkeley: Elettricità e Magnetismo, Zanichelli

5) D. Halliday, R. Resnick, K.S. Krane, Fisica, vol. II (III o IV edizione), Ambrosiana

6) E. Amaldi, R. Bizzarri, G. Pizzella, Fisica Generale, Zanichelli

Testi consigliati per le esercitazioni:

7) F. Porto, G. Lanzalone, I. Lombardo, Problemi di Fisica Generale – Elettromagnetismo e Ottica, EdiSES

8) M. Bruno, M. D’Agostino, R. Santoro, Esercizi di Fisica: Elettromagnetismo, Ambrosiana