The goal is the acquisition of the basic principles, physical meanings and experimental evidences of the classical electromagnetism as described by the Maxwell’s equations (both in integral and differential form). Electrostatics, magnetostatics, induction and wave propagation phenomena are treated with special emphasys. The ability to autonomously apply the acquired knowledge to the analysis and solution of stationary, time dependent and wave propagation electromagnetic problems is an important expected skill outcome. 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 which are at the basis of many engineering problems.

Good knowledge and mastery of the mathematical instruments learnt in the course of Mathematical Analysis I and II and of Geometry are required. Tools and concepts from the course of Physics I are an important prerequisite. In particolar, Electrostatics in vacuum is treated in the Physics I course and must be known at the beginning of the this course, being fundamental for the comprehension of all the Physics II topics.

Vector Calculus Scalar and vector fields. The nabla operator. Gradient, divergence, cross product. Flux and circulation of a vector field. Gradient theorem, Gauss' and Stokes' theorems. Continuity equation. Stationary electric fields 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. Polarization of matter, the electric displacement vector. Capacity and capacitors. Energy of the electric field. Conductivity, Ohm's law, resistors, Joule's effect. The electromotive force. Stationary magnetic fields Magnetic force on a moving charge, Lorentz's force, motion of a charge in a uniform magnetic field. Cyclotron, mass spectrometer, the classical Hall effect. Magnetic force on electric currents, magnetic torque on rectangular and any shape circuits, magnetic dipole. Orbital and spin magnetic dipole. Sources of magnetic field: Ampère-Laplace's law, application to rectilinear (Biot-Savart's law, forces between currents) and circular loops. The indefinite solenoid, results for the finite solenoid. Ampère’s law. Gauss' law for the magnetic field. Magnetization of matter: phenomenology, magnetic susceptibility, diamagnetic, paramagnetic and ferromagnetic materials, first and second Curie's law, magnetic hysteresis. Maxwell’s equations in differential and integral forms for static fields. Time-dependent fields Electromagnetic induction, Faraday's law, relative motion of conductor and magnetic field. Self-induction. Transients: first-order circuits, RL and RC. Coupled circuits, mutual-induction. Energy of the magnetic field. The principle of conservation of charge, Ampère-Maxwell's law. Maxwell’s equations in differential and integral forms for time-dependent fields in vacuum and in matter. Electromagnetic waves Wave phenomena. Plane electromagnetic waves as solutions of Maxwell's equations. Energy, momentum, Poynting vector. Radiation pressure. Polarization of electromagnetic waves. Electromagnetic spectrum. Elements of wave propagation Laws of reflection and refraction, absolute and relative refraction index, total reflection. Wave propagation phenomena; interference phenomena.

Class exercises include simple problem solving activities, with strict connections to theoretical lectures. The procedure of exercise solution is aimed at developing specific analysis methodology and calculus techniques.

Lectures: reference text P. Mazzoldi, M. Nigro, C. Voci, Fisica, Elettromagnetismo - Onde, vol. II, EdiSES, Napoli, 2010. Lectures: supplemental texts (more detailed information will be given in class) - P. Mazzoldi, M. Nigro, C. Voci, Elementi di Fisica: Elettromagnetismo - Onde, vol. II, EdiSES , Napoli, 2010. - R. Marcon, Elementi di elettromagnetismo, CISU, 1991. - C. Mencuccini, V. Silvestrini, Fisica II - Elettromagnetismo e Ottica, Zanichelli Editore, 1999. - D.J. Griffiths, Introduction to Electrodynamics, Pearson, 2013. - H.D. Young, R.A. Freedman, A.L. Ford, Principi di Fisica-Elettromagnetismo e Ottica, vol. 2, Pearson, 2015. Exercises Text and solutions of the classroom exercises will be available online. The following exercises collections may be recommended (one at choice): - G. A. Ummarino, Esercizi svolti di Fisica II, CLUT, 2015. - P. Pavan, P. Sartori, Problemi di Fisica II risolti e commentati, Casa Editrice Ambrosiana, 3a edizione, 2006. - A. Tartaglia, Esercizi svolti di Elettromagnetismo e Ottica, Levrotto&Bella, Torino, 1998.

Exercise with solutions ;

You can take this exam before attending the course

Exam: Computer lab-based test; Compulsory oral exam;

MODE A (prof. Iotti and prof. Barbero) The examination consists of two parts (both compulsory): 1) first a test-on-line at the Politecnico's LAIB; 2) then an oral examination. 1) The LAIB test lasts one hour and consists of thirty multiple-answer questions, concernign both theoretical topics and exercises. Reservation is mandatory and is to be done online through the Portale della Didattica, according to the procedures and within the deadlines set out by the Politecnico Didactic Secretary. Students must show their personal Politecnico badge and a valid ID card to be admitted at the LAIB for the test. To start the test, students have to login with their personal Politecnico credentials. Consulting any kind of book or material is forbidden during the test. The LAIB test is a multiple-choice exam. A choice between five answers is given for each question: a right one (score +1) and three wrong ones (penalty score -1/3). The total test score PTEST is automatically calculated and shown immediately after submittance 15/30 or higher are admitted to the oral examination. Students with PTEST ≥ 15/30 are admitted to the oral examination, with a score P = PTEST + 3/30 (extra bonus). 2) Students with P ≥ 18/30 are admitted to the oral examination. In particolar: • if 18/30 ≤ P < 23/30, the student can perform only a validation oral exam, whose final grade ranges from failure to P; • if P ≥ 23/30, the student can choose between the validation oral exam (with highest possible final grade 23/30) and a traditional oral exam (final grade ranging from failure to 30/30 e lode). Please note: The oral exam must be taken within the same “appello” in which the LAIB test has been passed. After this deadline, the LAIB test score won't be valid any more and a new test must be passed. ----------------------------------------- MODE B (prof. Barbero) The exam is divided into: 1) a written test consisting of three exercises, mandatory; 2) a written test of theory, which consists of three questions, mandatory; 3) an optional oral exam. To access the theory test, the test score on the exercises must be greater than or equal to 15/30. The exercises will be taken from those proposed in the book P. Mazzoldi, M. Nigro, C. Voci, Elementi di Fisica: Elettromagnetismo - waves, vol. II, EdiSES, Napoli, 2010. Questions related to the theory test will be communicated before the Christmas holidays. To pass the exam also the theory test must be sufficient. The final grade will be the arithmetic average, approximated by excess, of the two tests. N.B. The tests must be all taken within the same 'appello'.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.