( english version )
Physics 2 ( 6 CFU )
Prof. Stefano Carretta
     Tel. +39 0521 905218 - Fax. +39 0521 905223           E-mail. stefano.carretta@fis.unipr.it

This course aims to give to the students the basic knowledge on electromagnetism, general
properties of waves, in particular mechanical and electromagnetic waives and principles of
geometric and wave optics.

1 Electromagnetism
1.1 Current and resistance. Resistance and Ohm law –The Drude’ s model –Parallel and series
resistances – Voltmeters and Amperometers
1.2 DC circuits. Batteries – Electric energy – Kirchhoff laws – RC circuit.
1.3 Magnetostatic. History – Magnetic field - Oersted, Ampère, Biot e Savart experiments-
Lorentz force – Force on a current - Ampère law – Ampère law applications: linear wire, coil,
planar current – Mass spectrometer – Force between currents – Field generated by a coil – Dipolar
field – Particles motion in a magnetic field -
1.4 Magnetic induction. Faraday-Lenz law – induced efm – Motors and generators – Transformers
and inductances – Reciprocal induction coefficient – Self induction – Magnetic energy.
1.5 Alternated currents. RL circuit – Oscillations in a LC circuit - RLC circuit.
1.6 Maxwell equations. Displacement current - Maxwell equations – Oscillating circuit and the
antenna - Electromagnetic radiation - Poynting vector- Radiation pressure and intensity.

2. Waves
2.1 General properties of wave motion
Wave characteristics. Longitudinal and transverse waves. Wave Fronts. Wave function. General
wave equation. Phase. Phase velocity. Sinusoidal waves.
2.2 Superposition of waves
The principle of superposition. The Fourier theorem. Interference of sinusoidal waves. Standing
waves. Beats. Propagation in dispersive media: group velocity.
2.3 Propagation of mechanical transverse and longitudinal waves
The speed of a transverse wave in a tight string. Equation of the transverse wave. Energy flow
and wave intensity for a transverse wave. Reflection and refraction of transverse waves in a
string. Transverse standing waves in a string. The speed of a longitudinal wave in the ideal gas.
Propagation of acoustic waves.
2.4 Electromagnetic waves
Mathematical derivation of electromagnetic wave equation from the Maxwell’ s equations. Plane
electromagnetic wave. Polarized waves: linear, circular and elliptical polarization. Spectrum of the
electromagnetic waves.
2.5 Energy and momentum of electromagnetic waves
The Poynting vector. Intensity of an electromagnetic wave. Momentum of an electromagnetic
wave and radiation pressure.
2.6 Sources of electromagnetic waves


Norberto Vignali

Il presente documento è di proprietà CEDI. A termine di legge ogni diritto è riservato.

Radiation from an oscillating electric dipole. Short account of radiation from accelerated charges.
2.7 Propagation of electromagnetic waves in matter
Refraction index. Propagation of electromagnetic waves in dispersive media: (1) dielectrics and (2)
system of free charges.

3. Optics
3.1 The light
Double nature of the light. Huygens’ s principle. Introduction to the concept of ray. Fermat’ s
3.2 Wave geometry: plane surfaces
Reflection and refraction of electromagnetic waves at plane surfaces. Derivation of the reflection
and the refraction laws from the Huygens’ s principle. Dispersion and prisms. The total reflection.
3.3 Wave geometry: spherical surfaces
Reflection and refraction at spherical surfaces. Lenses. Optical systems: the microscope and the
3.4 Polarization
Methods to obtain linearly polarized waves: (i) selective absorption (dichroism), (ii) reflection at
the Brewster angle, (iii) diffusion.
3.5 Interference
Coherence. Interference of waves produced by two synchronous sources. Interference of several
synchronous sources. Interference due to a thin layer. Michelson interferometer.
3.6 Diffraction
Fraunhofer diffraction by a rectangular aperture. Resolving power. Fraunhofer diffraction by two
equal parallel slits. Diffraction grating.

Attività d'esercitazione
Theoretical lessons will be completed with practical ones consisting into the assisted solution of
exercises on the treated arguments.

Modalità d'esame
The students who constantly attend the lessons and get a pass on the infra annum tests, can take a
simplified final exam. The others will have to take a complete one which consists of a written and,
if required, an oral test.

Fisica Generale I

Testi consigliati
W.E. Gettys, F.J. Keller, M.J. Skove, Fisica classica e moderna 2. McGraw-Hill Libri Italia,
Milano, 1998

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