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CODICE 65940 2016/2017 6 cfu anno 2 INGEGNERIA BIOMEDICA 8713 (L-8) - ING-INF/02 Italiano 2° Semestre AULAWEB

## OBIETTIVI E CONTENUTI

### OBIETTIVI FORMATIVI

Campo elettromagnetico nel vuoto: eq. di Maxwell per il vuoto, forme locali e forma globali; campo elettromagnetico in presenza di materia; circuiti a parametri concentrati; principi di Kirchhoff e loro limiti di validità; onde elettromagnetiche; circuiti a parametri distribuiti.

### MODALITA' DIDATTICHE

Le lezioni e gli esercizi vengono svolti dal docente in aula.

### PROGRAMMA/CONTENUTO

• Course organization and overview of its contents (1; 1)
• Some comments on Newtonian, relativistic and quantum physics; the role of classical relativistic electrodynamics in modern physics; some links between classical relativistic and quantum electrodynamics in simple cases; some properties of photons; number and properties of photons involved in many engineering applications (3; 4)
• Recalling some prerequisites: Lorentz force; different models for electric charge distributions; electric current and electric current density; conservation of charge; Maxwell's equations in the presence of charges in vacuum in integral form (2; 6)
• Exercises related to scalar and vector fields, circulations, fluxes, differential operators, international system of units (for electromagnetic quantities); foundamental equations in the presence of charges in vacuum in differential form (3; 9)
• Electromagnetic fields in the presence of ponderable media:
1. Some considerations on the constituents of matter (0.5; 9.5)
2. Drawbacks of the approach based on the microscopic Maxwell's equations and the need for macroscopic quantities and relationships among them (0.5; 10)
3. Conduction current: charge carriers; carrier concentration; its value in solids (conductors, semiconductors, insulators), liquids (electrolytes), gases (e. g., ionosphere, plasma); convection currents; conduction currents in the presence of a single family of carriers; different contributions to the velocity of carriers: thermal, diffusion and drift velocity; Fick's first law; diffusion coefficient; carrier drift; carrier drift in the presence of an electric field; carrier mobility; some important values for the carrier mobility; effects of the temperature on the mobility and on carrier concentration; conductivity; its values in most important materials; unit of measures; first simple constitutive relation for the current density; ideal insulators; superconductors and perfect electric conductors; conduction current in the presence of more families of carriers; other types of current (1.5; 11.5)
4. Exercises related to electrostatics: electric field and scalar potential due to point charges, line, surface or volume distributions of charges, dipoles and ideal dipoles, distributions of dipoles (1; 12.5)
5. Electric polarization: electric dipole moments; electric dipole moment density (electric polarization or dipole moment per unit volume); surface and volume charge densities equivalent to the distribution of dipoles (1.5; 14)
6. Some examples of dipole distributions; electronic polarization, atomic-ionic-molecular polarization and polarization due to the orientation of polar molecules; examples: Bohr's atomic model, ethylene molecule, water molecule; macroscopic effect of polarization-charge densities; generalization of Gauss theorem; generalization for time-varying electromagnetic fields; electric displacement; first generalization of Ampere-Maxwell law (3; 17)
7. Exercises related to magnetostatics: fundamental laws; vector potential; vector potential due to surface or linear current densities (1; 18)
8. Magnetic polarization: magnetic dipoles; ideal magnetic dipoles; magnetic dipole moment; magnetic dipole moment density per unit volume (magnetic polarization or magnetic dipole moment per unit volume); linear and surface current densities equivalent to the distribution of magnetic dipoles (1.5; 19.5)
9. Some examples of magnetic dipole distributions; diamagnetic, paramagnetic and ferromagnetic materials; macroscopic effects of polarization-current densities; final form of Maxwell's equations (integral and differential forms); macroscopic fields; displacement current (1.5; 21)
• Exercises: importance of curl and divergence equations; time-harmonic Maxwell's equations (1; 22)
• Constitutive relations for ponderable media: linear-non linear; isotropic-anisotropic; dispersive-non dispersive in space and time; homogeneity-inhomogeneity in space and time; examples; integration of time-harmonic Maxwell curl equation and constitutive relations for linear, stationary and spatially non-dispersive media; effective permittivity (3; 25)
• Boundary conditions at motionless interfaces between different media: conditions for the normal components of the electric dispacement, of the magnetic induction and of the Poynting vector; conditions for the tangential parts of the electric and magnetic fields (3; 28)
• Extension to electromagnetic phenomena of the principle of energy conservation
1. Poynting's theorem; physical meaning of the terms appearing in Poynting theorem (3; 31)
2. Exercises: exchange between electromagnetic energy and mechanical or thermal energy; Nichols' disk; Joule effect in a cylindrical conductor (2; 33)
3. Poynting theorem for time-harmonic fields (2; 35)
4. Exercises: power losses due to Joule effect and to dielectric losses; thermal effects in microwave ovens; field amplitudes radiated by isotropic antennas in a lossless and homogeneous medium (3; 38)
• A comment on the conservation of momentum and angular momentum in the presence of charged particles and electromagnetic fields (1; 39)
• Uniqueness theorem for the electromagnetic field: general case and time-harmonc case; importance of boundary conditions and of initial conditions; electromagnetic boundary value problems and Cauchy problems (3; 42)
• Electromagnetic waves
1. Electromagnetic fields in simple homogeneous media without charge carriers and impressed current densities: wave equation (1; 43)
2. Wave equation in one spece dimension: general form of its solution (2; 45)
3. Progressive and regressive plane waves; their expressions for a generic direction of propagation (1; 46);
4. Electromagnetic plane waves: TEM waves; general expressions for the electric and magnetic fields; speed of light as the velocity of propagation of electromagnetic plane waves; an additional comment on the special theory of relativiry (2; 48)
5. Other possible waves: spherical waves (1; 49)
6. Monochromatic plane waves; wavelength, wavevector, polarization of time-harmonic vectors and vector fields and its practical consequences (polarization division multiplexing, stereoscopic vision, etc.) (3; 52)
7. Propagation of plane waves in the presence of absorption: low loss dielectric media and good conductors; attenuation; skin depth; velocity of propagation; some comments on the effects of dispersive media (3; 55)
8. Reflection and transmission of a monochromatic plane wave at a plane interface: the case of orthogonal incidence (reflection and transmission coefficients; interference; behaviour of the magnitude of the electric field; standing waves; standing wave ratio; measures of the reflection coefficient and of the intrinsic impedance of a material; reflection by an ideal mirror; consequences and applications of interference: Young experiment, simple phased arrays) (3.5; 58.5)
9. Fabry-Perot resonant cavity (qualitative description) and its applications (0.5; 59)
• Some comments on the biological effects of electromagnetic fields, electromagnetic dosimetry, electromagnetic field measurements and safety standards to protect EU citizens (3; 62)

### TESTI/BIBLIOGRAFIA

Note disponibili sul sito di Ingegneria Biomedica, da integrare e completare. G. Conciauro, L. Perregrini, ‘Fondamenti di onde elettromagnetiche’, McGraw-Hill, Milano, 2003.

## DOCENTI E COMMISSIONI

### Commissione d'esame

MIRCO RAFFETTO (Presidente)

GIAN LUIGI GRAGNANI

MATTEO PASTORINO

ANDREA RANDAZZO

## LEZIONI

### Orari delle lezioni

CAMPI ELETTROMAGNETICI

## ESAMI

### MODALITA' D'ESAME

Durante l'esame orale vengono poste tre domande, di cui almeno una di tipo teorico e almeno una formulata come un esercizio.

### MODALITA' DI ACCERTAMENTO

Risultati d’apprendimento previsti: Il corso dovrebbe mettere gli studenti in grado di comprendere i principi dell’elettromagnetismo e di affrontare problemi non troppo complessi in tale materia.

### Calendario appelli

Dati Ora Luogo Tipologia Note
29/05/2017 10:00 GENOVA Orale lunedì 9 gennaio 2017 - Aula E4, Nel pomeriggio E2 mercoledì 25 gennaio 2017 Aula E3 venerdì 10 febbraio 2017 Aula E3 lunedì 29 maggio 2017 - Aula E3 lunedì 19 giugno 2017 - Aula E3 venerdì 28 luglio 2017 - Aula E3 venerdì 15 settembre 2017 - Aula E3
14/06/2017 11:00 GENOVA Orale giovedì 22 dicembre 2016 - Aula G2b giovedì 12 gennaio 2017 - Aula G2b giovedì 2 febbraio 2017 - Aula G2b giovedì 16 febbraio 2017 - Aula E4 mercoledì 14 giugno 2017 - Aula G2b venerdì 14 luglio 2017 - Aula G2b lunedì 11 settembre 2017 - Aula G2b
19/06/2017 10:00 GENOVA Orale lunedì 9 gennaio 2017 - Aula E4, Nel pomeriggio E2 mercoledì 25 gennaio 2017 Aula E3 venerdì 10 febbraio 2017 Aula E3 lunedì 29 maggio 2017 - Aula E3 lunedì 19 giugno 2017 - Aula E3 venerdì 28 luglio 2017 - Aula E3 venerdì 15 settembre 2017 - Aula E3
14/07/2017 10:00 GENOVA Orale giovedì 22 dicembre 2016 - Aula G2b giovedì 12 gennaio 2017 - Aula G2b giovedì 2 febbraio 2017 - Aula G2b giovedì 16 febbraio 2017 - Aula E4 mercoledì 14 giugno 2017 - Aula G2b venerdì 14 luglio 2017 - Aula G2b lunedì 11 settembre 2017 - Aula G2b
28/07/2017 10:00 GENOVA Orale lunedì 9 gennaio 2017 - Aula E4, Nel pomeriggio E2 mercoledì 25 gennaio 2017 Aula E3 venerdì 10 febbraio 2017 Aula E3 lunedì 29 maggio 2017 - Aula E3 lunedì 19 giugno 2017 - Aula E3 venerdì 28 luglio 2017 - Aula E3 venerdì 15 settembre 2017 - Aula E3
11/09/2017 10:00 GENOVA Orale giovedì 22 dicembre 2016 - Aula G2b giovedì 12 gennaio 2017 - Aula G2b giovedì 2 febbraio 2017 - Aula G2b giovedì 16 febbraio 2017 - Aula E4 mercoledì 14 giugno 2017 - Aula G2b venerdì 14 luglio 2017 - Aula G2b lunedì 11 settembre 2017 - Aula G2b
15/09/2017 10:00 GENOVA Orale lunedì 9 gennaio 2017 - Aula E4, Nel pomeriggio E2 mercoledì 25 gennaio 2017 Aula E3 venerdì 10 febbraio 2017 Aula E3 lunedì 29 maggio 2017 - Aula E3 lunedì 19 giugno 2017 - Aula E3 venerdì 28 luglio 2017 - Aula E3 venerdì 15 settembre 2017 - Aula E3