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

To effectively complete the Physics 2 course and achieve the expected learning outcomes, students must possess the following preliminary knowledge and skills: - Mathematics Prerequisites: Mathematical Analysis: Differential and integral calculus in one and more variables, partial derivatives and gradients of scalar functions, line, surface, and volume integrals, first- and second-order ordinary differential equations Linear Algebra and Geometry: Vector calculus (dot product, vector product, mixed product), operations with vectors in Cartesian coordinates Complex Analysis (Basic Elements): Complex numbers and exponential representation, algebraic operations with complex numbers - Physics Prerequisites (Classical Mechanics, Physics 1): Kinematics and dynamics of particles and systems, principles of energy conservation and the concept of potential energy, oscillatory motion - Methodological Skills Problem Solving: Ability to set up and solve quantitative physics problems, proficiency in the use of units of measurement and dimensional analysis Representation Graphics: interpretation and construction of function graphs, vector representation of physical quantities Recommended Basic Knowledge Elements of Chemistry: atomic structure and properties of elements, chemical bonds, and the structure of matter Previous courses in Physics 1, Geometry, Calculus 1, and Calculus 2 are required.

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

Assessment Structure Written Exam: Solving numerical problems on the main topics of the program (exercises calculating electric fields for specific geometric configurations, analysis of the motion of objects in the presence of magnetic fields, quantitative analysis of DC and AC circuits, problems in geometric and physical optics (reflection, refraction, interference, diffraction). Duration: 4 hours Assessment: up to 30 points Oral Exam: Discussion of the fundamental theoretical topics of the course, assessing the student's ability to connect topics from different sections of the course and their ability to express themselves in scientifically correct language. Duration: 15 minutes of discussion and 60 minutes of writing per student. Assessment: up to 30 points Assessment of Group Activities: The topics developed during group work will be assessed based on the quality of their analysis, ability to summarize and present clearly, their contribution to the class discussion, and their active participation. Assessment: up to 12 Points Assessment Criteria Knowledge and Understanding (40%): Mastery of fundamental theoretical concepts Understanding of physical laws and their interconnections Knowledge of the properties of materials and electrical devices Application Skills (40%): Ability to solve quantitative problems Correct use of mathematical and physical methods Ability to choose the most appropriate solution approach Communication Skills and Independent Judgment (20%): Clarity of presentation and correct use of scientific language Ability to critically argue Quality of group work and presentations Passing Criteria To pass the exam, the following is required: A minimum score of 15/30 in each test (written and oral) Demonstration of a sufficient understanding of fundamental physical principles Ability to solve basic problems on all the main topics of the program Active participation in teaching activities and completion of group work Final Grade: Average A weighted written and oral exam, plus the grade for group activities. Further information is available on the course website: https://sites.google.com/uniroma1.it/fisica2-sarti/home

The Physics 2 course adopts an integrated teaching approach that combines lectures, participatory discussions, and collaborative activities: - Lectures and Teaching Materials Lectures are based on structured teaching materials made available to students, including: Slides presenting theoretical topics In-depth documents for independent study and critical analysis of content Supplementary materials for in-depth exploration of specific topics - Class Discussions A significant portion of class time is dedicated to participatory discussion of teaching materials, with the aim of: Stimulate critical discussion of theoretical content Encourage active development of knowledge among students Clarify complex aspects through teacher-student dialogue Connect theoretical principles to practical and technological applications - Group Activities Students are organized into working groups to develop specific topics from the program. This methodology allows for: Promoting collaborative learning and peer discussion Developing research, analysis, and synthesis skills Encouraging independent study and in-depth analysis Stimulating communication skills through the presentation of group work results Encouraging critical discussion and collaborative problem-solving The alternation between lectures, guided discussions, and group work is designed to: Consolidate theoretical foundations through structured explanations Developing critical analysis skills through participatory discussion Applying acquired knowledge through independent development of specific content Promoting active and informed learning that prepares students for the professional challenges of engineering