Electronics Engineering

MAURO MIGLIORATI
ENRICA CHIADRONI

GENERAL
The module provides: the basic principles of electromagnetism, with particular reference to the concept of field and Maxwell's equations, and lays the basics for the understanding of electrical, magnetic, wave and optical phenomena.

SPECIFIC
• Knowledge and understanding: to know analytical methods for solving basic problems of electrostatics and magnetostatics and of simple circuits in direct currents. The student will also be able to understand the basic principles of electromagnetic induction and the propagation of electromagnetic waves.
• Applying knowledge and understanding: the student will be able to model some simple phenomena related to electric and magnetic fields. During the course some laboratory experiences on measurements of stationary and quasi-stationary currents and geometric optics are provided. At the end the student will be able to use a digital multimeter and will have acquired the ability to process experimental data through the basic tools of statistics and measurement theory.
• Critical and judgmental skills: the student will have to bring to the exam the reports regarding the laboratory experiences, that will be illustrated. During the exam, the student is also required to be able to connect between different electrical and magnetic phenomena addressed in the course and to acquire a more general view of the various aspects of electromagnetism.
• Communication skills: knowing how to describe electrical and magnetic phenomena, knowing how to illustrate Maxwell's equations with understandable concepts with a minimum of technical background. Communication skills are also achieved by addressing some fundamental issues of physics, such as conservation principles, also on the basis of the knowledge acquired in the courses already passed.
• Learning skills: ability to continue subsequent studies on advanced topics of electromagnetism, based on the analysis and modeling methodologies acquired during the course.

Level 1 - knowledge and comprehension
Students will be able to explain the principles of electrostatics in a vacuum, including Coulomb's law, electric field, and electric potential.

Level 2 - Application of knowledge and understanding
Students will be able to apply electrostatic concepts to solve problems related to electric fields generated by charge distributions.

Level 3 - Autonomy in knowledge management
Students will be able to design and conduct experiments to measure quantities related to electric circuits.

Level 4 - Problem solving and decision making skills
Students will be able to solve complex problems related to electrostatics in conductors and dielectrics, and apply Ohm's law in direct current circuits.

Level 5 - Communication and lifelong learning skills
Students will be able to effectively communicate the results of their experimental analyses and will be prepared for continuous learning in the fields of physics and engineering.

Level 6 - Advanced problem solving skills and critical application of knowledge
Students will be able to analyze and solve advanced problems related to electromagnetic induction and electromagnetic waves.

Mathematical analysis 1 is requested as prerequisite.

It is strongly suggested to take the examination of physics I before physics II.

The student must know the basic concepts of mechanics of the material point and systems.
The student must also know the concepts of function, derivative, integral and operations between vectors.

25 hours:
Electrostatics in vacuum - Electric and Potential field.
Electric force; electric charge and Coulomb's law; the electric field; electrostatic field generated by some charge distribution. Gauss theorem; the first Maxwell equation; the electric potential. The electric dipole; mechanical actions on electric dipoles in an external electric field. Rotor of a vector field. The conservativeness of the electrostatic field.
Systems of conductors and electrostatic field. Electrostatic field and charge distributions in conductors. Electric capacity. Capacitor systems; energy of the electrostatic field. Mechanical actions of an electrostatic nature in conductors. The general problem of electrostatics in some cases.
Electrostatics in the presence of dielectrics.
The dielectric constant; microscopic interpretation. Vector electric polarization (or polarization intensity). The electrostatic equations in the presence of dielectrics; The general problem of electrostatics in the presence of dielectrics and boundary conditions; electrostatic energy in presence of dielectrics; Electrostatic machines.

15 hours:
Direct electric current.
Conductors; electric current; current density and continuity equation. Electric resistance and Ohm's law; dissipative phenomena in conductors; electromotive force and electric generators. Electrical resistance of ohmic conducting structures; DC circuits. Superconductors; methods of current measurement, voltage and resistances; charges on current carrying conductors; quasi-stationary circuits.

15 hours:
Stationary magnetic phenomena in a vacuum. Lorentz force and magnetic induction vector; mechanical forces on circuits with stationary current in an external magnetic field.
Magnetic field generated by stationary currents in a vacuum; properties of the magnetic induction vector in the stationary case. Vector potential. Interactions between circuits with stationary currents; Hall effect.
Magnetism in matter.
General introductory considerations. Magnetic polarization and its relations with microscopic currents. The fundamental equations of magnetostatics in the presence of matter and the boundary conditions for the magnetic fields; macroscopic properties of dia-, para- and ferro-magnetic materials. Magnetic circuits, electromagnets and permanent magnets.

15 hours:
Time-varying electric and magnetic fields. Third and fourth Maxwell equation.
Electromagnetic induction. Faraday-Neuman law; physical interpretation of the phenomenon of electromagnetic induction; local form of the law of Faraday-Neumann and expression of the third Maxwell equation in the non-stationary case; self-induction and the coefficient of self-induction Mutual induction. Energy analysis of an RL circuit. Magnetic energy and mechanical forces. Electrogenerators and electric motors; the fourth Maxwell equation in the non-stationary case.

15 hours:
Electromagnetic waves.
Introductory considerations; some insights related to Maxwell's equations. Equation of electromagnetic waves. Plane electromagnetic waves. Spherical electromagnetic waves. Spectrum of electromagnetic waves; energy conservation and Poynting vector.
Electrodynamic potentials. Lorentz Gauge. Radiation of an oscillating dipole.
Classical phenomena of interaction between radiation and matter.
Conditions for connecting the between two materials; reflection and refraction of electromagnetic waves. Kinematic characteristics of the reflected wave and the refracted wave. Snell's law.
Light scattering. Natural light and polarized radiation. Huygens-Fresnel principle and Kirchhoff theorem. Interference. Young's experiment. Diffraction: introductory considerations. Fraunhofer diffraction from a slit.

10 hours:
Outline of Modern Physics. Superconductors. Special relativity and electromagnetism.

25 hours:
Didactic laboratory experiences with written reports
Measures in direct current.
Measurements of an RC circuit with multi-meter.
Measurements of an RC circuit with oscilloscope.
Measurements of a Dc circuit by means of Thevenin.
Geometric Optics.

C. Mencuccini e V. Silvestrini, Fisica II – Elettromagnetismo – Ottica, Zanichelli

Lecture notes on measurement theory
Exam exercises of previous sessions

Explanation of the theory lessons and carrying out of exercises that follow the course program on a classic blackboard, interactive white board, tablet with projection in the classroom, or through presentations.

The laboratory experiments will be carried out directly by the students under the supervision of the teacher.

Frequency is optional. If a student has not been able to carry out laboratory experiments for some reason, recovery days are to be arranged with the teacher.

Expected learning outcomes:
Knowledge of the basic phenomena of electricity and magnetism and ability to deal with problems of electrostatics and magnetostatics and simple circuits in continuous current. Knowledge of Maxwell's equations and ability to identify the underlying physical principles. Knowledge and ability to solve problems of quasi-stationary circuits with capacitors and inductors. Knowledge of the main phenomena of magnetic induction, and ability to solve simple problems related to the electric and magnetic fields varying over time. Knowledge of phenomena related to the propagation of electromagnetic fields and ability to solve problems related to reflection, refraction and interference of electromagnetic waves.

Assessment tools:
Written test and oral exam. The written test consists of 4 exercises and 2 theory questions. The duration of the written test is 2.5 hours. No material can be used during the written test.
The oral exam consists of three questions. Among the questions of the oral exam, questions related to the laboratory experiences carried out during the course may also occur. At the oral exam the student will have to bring the reports related to the laboratory experiences he has done during the course.

Assessment methods: verification of the student's ability to understand and be able to apply the fundamental laws that regulate electrical and magnetic phenomena. A typical exam consists in: verification of the degree of knowledge of Maxwell's equations and their derivation, verification of the ability to deal with and solve typical problems of electrostatics and magnetostatics and exercises with simple circuits that have been carried out during the lessons, verification of the level of knowledge related to the phenomena of electromagnetic induction, both from the theoretical point of view and through simple exercises, verification of the typical phenomena of electromagnetic waves: transported power, reflection, refraction and interference.

Evaluation criteria:
Each exercise of the written test is worth 6 points and each theory question is worth 3 points. The written test is considered passed if the student reaches the mark of 18. Each theory question at the oral exam is worth 10 points. The final mark is an average between the written and oral test marks.

Past examination exercises can be found on the website:
https://www.dropbox.com/sh/h50zlus8itk54c1/AADDnxDcyfbcg6YWt48s0fIQa?dl=0

• Introduction, electric actions, electric charges, Coulomb's law, Electric field
  • Books: Chapter 1


• Electric field generated by systems of charges, charge density, exercises on the electric field: infinite wire
  • Books: Chapter 1


• Gauss's theorem, electric field from distribution with spherical symmetry
  • Books: Chapter 1


• Divergence of a vector field, 1 Maxwell equation, electric field of an infinite wire with Gauss, of a full and empty cylinder, of a coil and of an infinite plane (without and with Gauss)
  • Books: Chapter 1


• The electric potential, definition of gradient, potential of charge distributions, potential of plane and infinite wire, rotor of the electric field
  • Books: Chapter 1


• E field from uniformly charged wire of finite length, potential and field on axis from charged disk and field from thick wall; force on point charge from semi-infinite linear distribution
  • Books: Chapter 1


• Gradient in spherical coordinates, the electric dipole, potential and electric field of the dipole, mechanical actions on electric dipoles: force and moment
  • Books: Chapter 1


• Mechanical actions on electric dipoles: potential energy. Conductors in equilibrium in the electrostatic field and their properties. Coulomb's theorem, electrostatic screen and power of the tips
  • Books: Chapter 1Chapter 2


• Capacitance of an insulated conductor, capacity of the earth, potential and induction coefficients, double layer, capacitors, capacity of flat, spherical and cylindrical capacitors
  • Books: Chapter 2


• Capacitors in series and in parallel, electrostatic energy of point charges, electrostatic energy of conductors and capacitors. Exercise: equilibrium distance of atom nucleus in external E


• Exercises on application of the principle of superposition of effects: E field in space from a uniformly charged cylindrical shell with vertical cut; E field in space from an infinitely charged plane with a circular hole; thick wall field with a vertical cylindrical hole
  • Books: Chapter 2


• Electrostatic energy density, electrostatic pressure and energy density, mechanical actions of an electrostatic nature in conductors, notes on Poisson's and Laplace's equations. Electric field on the infinite tape side
  • Books: Chapter 2


• Electric field in dielectrics, relative dielectric constant, polarization by deformation and orientation, polarization intensity vector
  • Books: Chapter 3


• Equations of electrostatics in the presence of dielectrics, electric field on the separation surface between two dielectrics, electrostatic energy with dielectrics, Van der Graaf generator
  • Books: Chapter 3


• Thermal and drift velocity in conductors, electric current, power transfer from the electric field to the current, current density. Exercise: spherical conductor with dielectric
  • Books: Chapter 4


• Exercises on capacitors with conducting plate between the plates; capacitive circuit; conducting sphere with cylindrical hole


• Continuity equation, Kirchhoff's laws, electrical resistance and Ohm's law, calculation of electrical resistances of structures, dependence of resistivity on temperature, local Ohm's law. Exercise: flat capacitor with dielectric in series
  • Books: Chapter 4


• Dissipative phenomena in current conductors, Joule's law also local, electromotive force and electric generators. Exercise: flat capacitor with dielectric in parallel
  • Books: Chapter 4


• Resistances in series and in parallel and equivalent resistance, generalized Ohm's law, mesh law. Exercises on networks, voltage and current divider.
  • Books: Chapter 4


• Thevenin and superposition theorem, measurements of currents, potential differences and resistances, insertion errors, Wheatstone bridge, quasi-stationary currents, discharge of a capacitor, flat and generic capacitor with lossy dielectric
  • Books: Chapter 4


• Electrostatic exercises with dielectrics: charged conducting sphere semi-immersed in oil; non-uniform dielectric cube; irregularly shaped charged conductor immersed in dielectric; capacitance of flat capacitor filled with dielectric; E field from a point charge in a plexiglass sphere


• Systematic and random errors and uncertainty, distribution function, mean value, variance and standard deviation, Chebyshev inequality, propagation of uncertainties, comparison between measurements: deviation, relative deviation and Student's t


• Least squares and examples, weighted average and result of various measurements with uncertainties, DC measurements, exercises: capacitor discharge, energy analysis of capacitor charging and discharging


• Lorentz force, and magnetic induction vector, applications: motion of a charge in a magnetic field, magnetic bottle, speed selector, mass spectrometer. Exercises on capacitor circuits with Thevenin
  • Books: Chapter 5


• Synchrotron, cyclotron, couple of forces on a coil in a uniform magnetic induction field, magnetic moment, Ampere's equivalence theorem.
  • Books: Chapter 5


• RC circuit exercises


• Magnetic field from stationary currents in vacuum, examples of magnetic field from stationary currents: infinite straight wire, tape, coil axis and equivalence with electric dipole, finite and infinite solenoid axis field.
  • Books: Chapter 5


• Properties of the magnetic induction field, Maxwell's II equation, linked flux, Ampere's circuitation theorem, Maxwell's IV equation in the stationary case, circuit exercises with Thevenin
  • Books: Chapter 5


• Vector potential, vector potential equation in the stationary case, Laplace's I formula through vector potential and its solution. Properties of the vector potential. Forces between rigid circuits, forces between two parallel wires and definition of the ampere.
  • Books: Chapter 5


• Maximum power transfer theorem with exercise (including Thevenin), discharge of a capacitor on another capacitor


• Explanation of laboratory experience on RC measurements. Magnetic field of an infinite solenoid, magnetic field of a charge in non-relativistic motion. Magnetic field of an infinite cylinder, hollow cylinder and perforated cylinder, Hall effect.
  • Books: Chapter 5


• Laboratory experience on direct current measurements


• Mechanical potential energy of a coil in a magnetic field. Suction force of a coil in a solenoid, magnetic induction field in the presence of materials, magnetization intensity, microscopic currents and relation with magnetization intensity vector
  • Books: Chapter 5Chapter 6


• Magnetic field and magnetic induction in the presence of materials, fields at the separation between two media, dia-para and ferro-magnetic materials
  • Books: Chapter 6


• Exercises on electrostatics with dielectrics and dielectric strength; calculation of the force on an electric dipole, dipole moment of two spherical distributions


• Faraday Neumann Lenz's law, cut flux and physical interpretation of Faraday Neumann Lenz's law
  • Books: Chapter 7


• Laboratory experiment on the charging of a capacitor


• Maxwell's III equation, self-induction coefficient for solenoid and bifilar line, study of an fRL circuit, opening and closing of a switch.
  • Books: Chapter 7


• Felici's Law, mutual induction and examples, Energy analysis of fRL circuit
  • Books: Chapter 7


• Ferromagnetic materials: Weiss domains, hysteresis cycle, Hopkinson's law, electromagnet, exercise on calculating B from an infinite gutter with Js
  • Books: Chapter 6


• Energy density of B, Foucault currents, electromagnetic brake and transformer, dynamos and alternators, instantaneous power and average power, motors, potential difference of a conducting rod rotating in B
  • Books: Chapter 7


• Oscilloscope presentation, Maxwell's IV equation in the non-stationary case and displacement current, inductance and magnetic energy of a coaxial cylinder carrying current
  • Books: Chapter 7


• Maxwell's equations, equation of electromagnetic waves
  • Books: Chapter 9


• Explanation of laboratory experience on RC+Thevenin, properties of plane electromagnetic waves
  • Books: Chapter 9


• Exercises: non-uniform current strip, B on the axis of two coils, magnet with air gap and magnetic circuits


• Exercises: Conducting ring in rotation with angular velocity parallel to the external B field. Disk dynamo; Application of Felici's law.


• Spherical waves, standing waves in the space between two ideal conductors, em waves in a conductor, penetration depth
  • Books: Chapter 9


• Electromagnetic wave spectrum, Poynting vector, instantaneous and average intensity of a wave.
  • Books: Chapter 9


• Connection conditions of electromagnetic fields, reflection and refraction of plane waves, kinematic characteristics, Fermat's principle, total reflection, optical fibers
  • Books: Chapter 10


• Explanation of laboratory experience on optics, interference, optical path, Kirchhoff's theorem and Huygens Fresnel's principle
  • Books: Chapter 10


• Laboratory experience on: RC with oscilloscope, Thevenin


• Application of the Faraday-Neumann-Lenz law, exercises on coils in a solenoid with variable B


• Young's experiment, exercises on interference, notes on diffraction, electric field of a solenoid with I(t), magnetic field of a discharging capacitor
  • Books: Chapter 10


• Exercises on em waves


• Electrodynamic potentials, notes on retarded potentials, the oscillating dipole: electric and magnetic fields at a long distance, Poynting vector and mean value
  • Books: Chapter 10


• Laboratory experience on optics


• Seminar on: Special relativity and electromagnetism (part 1)


• Seminar on: Special relativity and electromagnetism (part 2)


• Visit to Frascati National Laboratory


• Exam Review Exercises