( english version )

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

Finalità

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.

properties of waves, in particular mechanical and electromagnetic waives and principles of

geometric and wave optics.

Programma

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

Redazione:

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

principle.

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

telescope.

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.

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

Redazione:

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

principle.

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

telescope.

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.

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.

simplified final exam. The others will have to take a complete one which consists of a written and,

if required, an oral test.

Propedeuticità

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

Milano, 1998