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. Elecrtic 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. Monochromatic waves: wave period, wave length, wavenumber, wave vector and refractive index. Polychromatic light and white light: amplitude and phase spectrum. Spectral analysis. Spectrum of the solar light of a filament lamp and of a fluorescent lamp. Additive and subtractive colour synthesis. Spectrum of the fundamental colors.
10. The spectrum of the electromagnetic waves.Radio waves. Antennae. Diffraction. Propagation of the radio waves beyond the obstacles. Microwaves. Klystron and magnetron. The microwave oven. Infrared radiation. Visible radiation. Sources of visible light. Filament lamps and discharge lamps. Fluorescent lamps. Diffraction: wavelength used to read CDs, DVDs and BDs. Ultraviolet radiation. Electromagnetic quantum dependence on frequency. Ionization capacity of the high requency electromagnetic waves. X rays. Gamma rays.
11. Polarization of the electromagnetic waves. Tranversality of the electromagnetic waves. Relation between the elctric 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. Coherence matrix and degree of polarization. Application: anti-glare glasses, liquid cristals.
12. Geometrical optics. Diffraction and geometrical optic approximation: aperture angle of a beam due to the diffraction. Fresnel's diffraction phenomena. The light ray. Reflection, refraction and Snell's law. Huygens-Fresnel principle and mathematical formulation of Kirchhoff. Derivation of the laws of the reflection and the refraction from the principle of Huygens-Fresnel. Flat mirror. Prism. Spherical diopter. Gaus approximation. Diopter equation. Linear transversal magnification and angular magnification. Conjugate points and foci. Spherical mirror. Equation of the spherical mirror. Centred optical systems, simple lens, thin lens. The equation of the thin lens. Aberrations: spherical aberraton, coma, aberration of lateral object points with narrow pencils (astigmatism), curvature of the field of the image, distorsion, chromatic aberration. The eye. Accomodation. Reduced eye model.
13. Interference. The Young's experiment. Failure of the corpuscolar hypothesis of light and wave explanation. Constructive and desctructive interference. Required conditions for the interference. Coherence. Wavefront division and aplitude division interferometers. Coherence length. Fresnel mirrors, Fresnel biprism, Rayleigh interferometer, optical path, measurement of gas refractive indexes, interference by thin plates, Michelson interferometer.

Readings/Bibliography

• Copy of the transparencies presented during the course, available on World Wide Web at the URL:  https://lhcbweb.bo.infn.it/twiki/bin/view.cgi/GalliDidattica/GalliTrasparenze.
• Question and exercises for the assessment, available on World Wide Web at the URL: https://lhcbweb.bo.infn.it/twiki/bin/view.cgi/GalliDidattica/GalliDomandeEsercizi.
• Halliday, Resnick, Krane, Physics, volume 2, John Wiley & sons.
• Feynmann, Leighton, Sands, The Feynmann Lectures on Physics, vol II, Addison-Wesley.
• Amaldi, Bizzarri, Pizzella, Fisica Generale, elettromagnetismo, relatività, ottica, Zanichelli, Bologna.
• Bertin, Semprini Cesari, Vitale, Zoccoli, Lezioni di elettromagnetismo, Progetto Leonardo, Esculapio, Bologna.
• Rosati, Casali, Problemi di Fisica Generale, volume 2, elettricità, magnetismo, elettrodinamica e ottica, seconda edizione, Casa Editrice Ambrosiana, Milano.
• Salandin, Pavan, Problemi di Fisica risolti e commentati, volume 2, Casa Editrice Ambrosiana, Milano.

Teaching methods

• During the frontal lessons slides are shown by means of a projector connected to a PC.
• Such transparencies are made available to the students before the lectures by means of World Wide Web, in compact format (4 slides for page) and printable, in order to reduce the time and the work of mere transcription during the lessons.
• The proposed practices demand the use of the pocket calculator.

Assessment methods

• The examination consists of a written test.
• Tests are constituted by at least 3 problems resolve and at least 4 questions to answer.
• The assigned maximum time for the written tests is 90 minutes.
• Exercises are randomly chosen by a list of a few hundreds of exercises, available to the students through the World Wide Web (the last version available on the Web 15 days before the test is used). Their evaluation is based on their numerical results, which depend on a number randomly assigned to the students. The evaluation of the single exercise is 3/3 if the result is correct within 5 units of the third significant digit, is 2/3 if the result is correct within 10 units of the third significant digit, is 1/3 if the result is correct within 20 units of the third significant digit or if the mantissa of the result is correct within 5 units of the third significant digit but the exponent differs by one unit. In any other case the evaluation is 0/3.
  
• The questions are randomly chosen by a list of a few thousands of questions, available to the students through the World Wide Web (the last version available on the Web 15 days before the test is used). To each question is assigned a rating in the range 0-3.
• In order to participate to the written tests it is necessary to enroll itself in the lists available on the AlmaEsami system at least 8 (eight) days early with respect to the date of the examination.
• The exam of General Physics (C.I.) is passed if the average of the evaluation of the part A and B is greater than or equal to 18/30 and if the single evaluation is greater than or equal to 15/30. The two tests (part A and part B) must be passed in the same Academic Year. The registered mark is the average of the two marks.
  

Teaching tools

Projector, PC.

Links to further information

https://lhcbweb.bo.infn.it/GalliDidattica

Office hours

See the website of Domenico Galli