


Politecnico di Torino  
Academic Year 2017/18  
20AXPMK, 20AXPLX, 20AXPMQ Physics II 

1st degree and Bachelorlevel of the Bologna process in Energy Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Electrical Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Mathematics For Engineering  Torino 





Subject fundamentals
The aim of the course is to introduce the main physical principles related to the classical electromagnetism including the propagation of electromagnetic waves and principles of wave optics. The course provides insights on multidisciplinary topics related to electromagnetism giving special emphasis on the description of the experimental concepts and to several technological applications.

Expected learning outcomes
The goal is the acquisition of the basic principles related to electromagnetism, electromagnetic waves and optics.
The fundamental applications of each law are shown with the aim of providing the student with a method for the interpretation of the physical phenomena at the basis of many engineering problems. Ability to set up and solve physics problems at intermediate level, in the field of electromagnetism and waves. 
Prerequisites / Assumed knowledge
A good knowledge and mastery of the mathematical instruments learnt in the course of Mathematical Analysis I and II and of Geometry are required. Electrostatics in vacuum is treated in the Physics I course and must be known at the beginning of the Physics II course. This knowledge is fundamental for the comprehension of all the subjects that will be studied.

Contents
Stationary electric fields and electric current (18 hours)
A summary of: Coulomb's law, electric field and potential, motion of a charge in a uniform electric field. Discrete and continuous charge distributions. The electric dipole, force and torque on an electric dipole in an electric field. Gauss' law for the electric field, applications. Capacity and capacitors. Energy density of the electric field. Dielectric, polarization of matter. Conductivity, Ohm's law, resistors, Joule's effect. The electromotive force. RC circuits. Stationary magnetic fields (12 hours) Magnetic field and magnetic interaction. Force on a charge moving in a magnetic field. Magnetic force on a currentcarrying conductor. Sources of magnetic fields. Field of a straight currentcarrying conductor: Laplace’s law, and its applications. Magnetic field of a circular current loop. Magnetic dipole. Magnetic torque and potential energy of a magnetic dipole in a magnetic field. Forces between parallel currents. Ampère’s law and its applications. Magnetic fields in matter: diamagnetic, paramagnetic and ferromagnetic materials. Timedependent electromagnetic fields (12 hours) Faraday – Henry – Lenz law of electromagnetic induction and its applications. Inductance and selfinductance. RL circuits. Coupled circuits, mutualinduction. Energy density of the magnetic field. Principle of the electric charge conservation. AmpèreMaxwell law. Maxwell equations in differential and integral form. Electromagnetic waves (8 hours) Propagation of waves. Plane electromagnetic waves as solutions of Maxwell's equations. Energy and momentum of electromagnetic waves, Poynting vector. Radiation pressure. Polarization of light. Oscillating electric dipole. Electromagnetic spectrum. Waves propagation phenomena (10 hours) Laws of reflection and refraction, refraction index, total reflection. Interference: wave composition, coherent and incoherent sources, double slit Young's experiment. Fraunhofer's diffraction. Diffraction gratings. Photons. Technological applications. 
Delivery modes
The course consists of 45 hours of theoretical lessons and 15 hours of class exercises. Problems and exercises related to the lessons subjects will be solved in the tutorial classes.

Texts, readings, handouts and other learning resources
 Mazzoldi, Nigro, Voci, Elementi di Fisica, vol. 2, Elettromagnetismo e Onde, Edizione II, Edises
 Serway, Beichner 'Physics for Scientists and Engineers, Volume 2, Saunders College Publishing  Additional exercises will be supplied online by the teacher. 
Assessment and grading criteria
The goal of the exam is to test the knowledge of the candidate about the topics included in the program and to verify the skill in the understanding of the most important technological applications connected to the electromagnetic interaction and in the solution of problems. The exam involves a written and an optional oral proof. The written proof includes simple problems (either symbolic or numeric) and open questions about all the subjects of the course, to test ability in problem solving and a wide knowledge of the basic concepts on electromagnetism and optics. The total allotted time is 2 hrs. The written proof is passed with a total score of at least 18/30; the maximum score is 30/30. During the written examination, students can only use a portable calculator as a supporting material. The oral proof is about all subjects treated in the lectures and is mainly oriented to test the understanding of electromagnetism, electromagnetic waves and connected technological applications.
The final mark is a weighted average of written/oral scores. 
