Environmental Engineering

1. Electric and magnetic fields Electric charge, phenomenology and Coulomb's law. Concept of electric field. Calculation of E for simple charge configurations. Electric force acting on charges and dipoles. Flux of electric field through a closed surface. Theorem (or law) of Gauss (first Maxwell equation) and its local form. Electric potential. Third Maxwell's equation. Energy density associated with an electric field. Direct current and current density J. Equation of conservation of charge. Resistance and resistivity. Ohm's law. Force between current carrying wires. Lorentz force on a moving charge and definition of the magnetic field. Field generated by a current-carrying wire (Biot-Savart law). Laplace and Ampere-Laplace's law. Flux of B through a surface (second Maxwell equation) and divergence of B. Ampere's law and fourth Maxwell's equation. Use of symmetries for the calculation of the magnetic field (wire, toroid and solenoid). Force on a moving charge, on a Current-Carrying Wire and moment of forces on a coil traversed by current (electric motor). Electromotive force induced in a coil that moves in a static magnetic field. Modification of the fourth Maxwell equation in the presence of a time dependent electric field. Electromagnetic induction. Faraday's law and Lenz's law. Modification of the third Maxwell equation in the presence of a time dependent magnetic field. Induced currents. Self-induction and mutual induction. Inductance. Energy density associated with a magnetic field. Maxwell's equations and electromagnetic waves. Plane waves and spherical waves, Poynting vector. Huygens-Fresnel principle. Double-slit interference and diffraction grating. Fraunhofer diffraction by single slit. 2. Electrical circuits and devices Capacitors and resistors. Joule effect. Electromotive force. Kirchoff's laws. RL and RC circuits. General laws for the study of alternating current circuits. Method of complex numbers. Impedance. Energy aspects of the passage of alternating current circuits. Examples of devices that operate with electricity: electric motor, generator and transformer. 3. Electromagnetic fields in matter Conductors and insulators. Consequences of the Gauss theorem for conductive materials. Capacity of an insulated conductor and of two conductors (capacitor). Resistivity of a conductor from the microscopic point of view. Drude theory for conduction in metals. Resistance of inhomogeneous wires. Dielectric constant. Outline of the microscopic theory for the polarization of dielectrics. Fields P, E and D, susceptibility and relative dielectric constant. Maxwell's equations for the fields E and D. Capacity of capacitors wholly or partly filled with a dielectric. Magnetic fields in the presence of matter: classification of materials (diamagnets, paramagnets, ferromagnets) and microscopic causes of the difference between the various types of material. Fields M, B and H, magnetic susceptibility and permeability for dia-and paramagnetic materials. Hysteresis loop for ferromagnetic materials. Relations between fields at the interface between different media: interface continuity equations for the fields E, D, H and B. Electromagnetic waves in matter (weakly magnetic materials). Driven oscillator and effects on dielectric permittivity (frequency dependence and complex nature). Refractive index. Meaning of the real and imaginary part of the refractive index. Absorption of electromagnetic waves. Waves in presence of discontinuities. Case of normal incidence for insulators and conductors. Reflection of light by conductive materials. Snell laws for the reflection and refraction in the transition between media with different refractive index. Polarization of radiation and Brewster angle. Further information available on course site: https://sites.google.com/uniroma1.it/fisica2-sarti/home

Knowledge of the fundamental laws of physics (kinematics, principles of dynamics, concept of energy); Knowledge of basic mathematical tools (vector algebra; derivatives and integrals; differential equations) and their extension in three dimensions (surface and volume integrals, partial derivatives). It is necessary to have attended the courses of Physics 1, Geometry, Analysis 1 and Analysis 2.

P. Mazzoldi - M. Nigro - C. Voci Elementi di Fisica Vol. 2 - Elettromagnetismo e Onde casa editrice EDISeS or S. Focardi, I. Massa, A. Uguzzoni FISICA GENERALE - Elettromagnetismo FISICA GENERALE - Onde e Ottica Casa Editrice Ambrosiana Further information is available on the course website: https://sites.google.com/uniroma1.it/fisica2-sarti/home

face-to-face

There are two tests, one written and one oral, to be held within the same academic year, not necessarily within the same exam session. Both tests are based on open answers. The written test is intended to evaluate the student's ability to solve problems related to the topics covered during the course; the oral exam is used to evaluate the level of understanding of concepts and procedures that are the basis of the way in which the physical phenomena faced during the course are modeled. There are also ongoing tests (partially with closed answers, partially with open answers) which provide a score that is added to the evaluation of the written test. The purpose of these tests is to assess the degree of understanding during the course. The final grade corresponds to the arithmetic average between the grade of the written test (increased by the grade obtained in the ongoing tests) and the oral exam. Further information is available on the course website: https://sites.google.com/uniroma1.it/fisica2-sarti/home

Face-to-face lectures with exercises