PHYSICS II AND LABORATORY M - Z
Academic Year 2024/2025 - Teacher: ROSSELLA CARUSOExpected Learning Outcomes
- classical electromagnetism, both in the vacuum and in isotropic and homogeneous media;
- geometric and physical optics;
combined with the acquisition of the ability to solve problems of electromagnetism.
Another basic objective is the learning of the experimental method for the measurement of physical quantities in the laboratory and the check of physical laws.
Course Structure
Required Prerequisites
The main pre-requisites are: reference systems in Cartesian, polar and cylindrical coordinates; trigonometry; vector computation; integral and differential calculus with functions of many real variables. Furthermore, many topics of the Physics I course are fundamental.
Knowledge of vector differential operators is useful, however they are presented and used within the vector field lessons.
Attendance of Lessons
Detailed Course Content
ELECTROSTATICS
1.1 - Electrostatic force. Electrostatic field.
The composition of matter and the presence of electrical interactions between its charged constituents. Quantization and conservation of the electric charge. Insulating materials and conductors. Force between electric charges. Coulomb's law. The electrostatic field. Calculation of electrostatic fields for discrete and continuous distributions. The field map. Motion of a charge in an electrostatic field. Millikan experience.
1.2 - Electrical work. Electrostatic potential.
The electric work. The electric voltage. The electrostatic potential. The electrostatic energy. Calculation of potential and electrostatic energy: for a point charge and for discrete and continuous charge distributions. Potential energy of a charged system. Motion of a charge in an electrostatic field. Energy conservation. Motion in a central field. Classic model of hydrogen atom. Electrostatic separator and cathode ray tube. The electrostatic field as a potential gradient. Calculation of electrostatic fields from the potential for continuous charge distributions. The rotor of the electric field. Equipotential surfaces. Electric field and potential generated by a dipole. Motion of a dipole in a uniform electric field. Potential energy of a dipole placed in a field. Polar molecules.
1.3 - The law of Gauss.
Electrostatic flow. The Gauss law. Applications of the Gauss law: spherical shell, sphere, wire and uniformly loaded plane. The Gauss law in local form; Poisson and Laplace equations.
1.4 - Conductors. Dielectrics. Electrostatic energy.
Conductors. Electrostatic induction. Cable conductor. Electrostatic screen. Capacitors. Electrostatic energy.
Dielectrics. Relative dielectric constant, absolute, electrical susceptibility.
STATIONARY CORRENTS AND MAGNETOSTATIC FIELDS
2.1 - Electric current.
Electrical conduction. Average and instant current, current density. Ohm's law for ohmic conductors. Conductivity and resistivity. Classical model of conduction. Electrical resistance. Temperature dependence. Superconductors. Electricity and absorbed power. Generators of f.e.m. Resistors in series and in parallel. Kirchhoff's laws. RC circuit.
2.2 - Magnetic field.
Properties of magnets. Magnetic field. Lorentz force.
Magnetic force on a wire drawn by current: the second elementary law of Laplace. Torque agent on a current loop in a uniform magnetic field. Magnetic moment of astationary current loop. Hall effect. Motion of a particle in a uniform magnetic field. The speed selector. The mass spectrometer. The cyclotron.
2.3 - Sources of the magnetic field. Ampère's law.
Magnetic field produced by a current element - first elementary Laplace law.
Magnetic permeability of the vacuum. Ampere-Laplace law for the magnetic field generated by a closed current circuit. Magnetic field produced by a rectilinear wire (Biot-Savart law), by a circular coil, by an ideal solenoid. Forces acting on parallel wires driven by current. Ampère law. Gauss law for the magnetic field.
Displacement current. Ampère-Maxwell law. Magnetic properties of matter. Permeability and magnetic susceptibility.
CURRENTS AND VARIABLE FIELDS
3.1 – Time-dependent electric and magnetic fields. Faraday law. Lenz law. Current generators. Self-induction. Circuits RL. Magnetic energy. Density of magnetic energy. Maxwell equations.
3.2 - Ideal and dumped electrical oscillations. Alternating currents. Resistors, capacitors and inductors in AC.
ELECTROMAGNETIC WAVES
4.1 - Electromagnetic waves.
Electromagnetic waves. Harmonic electromagnetic waves. Linear, circular and elliptical polarization. Poynting vector. Intensity of a wave e.m. Radiation pressure. Electromagnetic spectrum. Spherical waves.
OPTICS
5.1 - Reflection and refraction of light.
Speed of light in a medium. Index of refraction. Cauchy formula. Principle of Huygens-Fresnel. Reflection and refraction. Limit angle. Total reflection. Chromatic dispersion. Prism. Fresnel coefficients. Brewster angle. Polarization by reflection. Polarization by selective absorption and diffusion. Malus law. Birefringence. Optical activity.
5.2 - Geometric optics.
Image construction in geometric optics. Spherical and flat mirrors. Focal distance. Magnification. Spherical and flat diopters. Dioptric power. Front and rear focal distances. Magnification. Thin lenses. Convergent power. Focal distance. Lens builder equation. Magnification. Optical microscope. Visual enlargement.
5.3 - Interference.
Interference from two slits. Minimum and maximum interference position. Intensity distribution between the fringes. Phase method for calculating intensities.
5.4 - 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.
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.
LABORATORY ACTIVITY
Measurement of the elastic constant of a spring.
Measurement of gravity acceleration with the simple pendulum.
Measurement of the viscosity coefficient of glycerine.
Resistance measurement with the voltamperometric method.
Measurement of resistances of high value, by means of the discharge of the capacitor.
Measurement of the ratio e / m by magnetic deflection.
Measurement of the focal distance of a converging lens.
Verification of the Malus law and measurement of concentrations of optically active solutes.
Measurement of wavelengths through a diffraction grating.
Textbook Information
1. P.Mazzoldi, N.Nigro, C.Voci: ELEMENTI DI FISICA, Vol.II - Elettromagnetismo e Onde, EdiSES Napoli
2. D. Halliday, R.Resnick: FISICA 2, Ed. Ambrosiana
3. R.A.Serway – Fisica Vol.II - ed.EdiSES
4. P.A.Tipler, G.Mosca - Physics for scientists and engineering, W.H.Freeman and Company
5. J. Taylor: Introduzione all'analisi degli errori. Lo studio delle incertezze nelle misure fisiche, Zanichelli
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Electrostatics | 1, 2, 3, 4 |
| 2 | Stationary currents and magnetostatic fileds | 1, 2, 3, 4 |
| 3 | Variable currents and fields | 1, 2, 3, 4 |
| 4 | Electromagnetic waves | 1, 2, 3, 4 |
| 5 | Optics | 1, 2, 3, 4 |
| 6 | Elements of Theory of Errors | 5 |
Learning Assessment
Learning Assessment Procedures
The written test lasts two hours and requires the resolution of three problems concerning electrostatics, e.m. time-varying fields and optics. Each problem is awarded 10 points and the minimum score for access to the oral exam is 18/30. With a score between 15 and 17/30 it is possible to request admission with reserve to the oral exam. The oral exam must be taken by the date on which the next written exam is scheduled. The evaluation criteria of the written test are: the correctness of the problem setting, the clarification of the identified resolution procedures, the correct determination of the numerical results associated with the units of measurement of the physical quantities in question.
At the end of the course, one of the experiences foreseen in the program of laboratory activities is drawn for each student; within one week the student will deliver the report, drawn up on the basis of the experience carried out and the personally acquired data. Taking into account the punctuality of delivery, the essay will be evaluated by the teacher on the basis of correctness, completeness, conciseness and properties of written expression.