# Elements of electromagnetics

## Learning outcomes of the course unit

At the end of the course the students will be able to:

− know the fundamental electromagnetic phenomena and their laws;

− understand the most important physical phenomena related to electromagnetism;

− solve exercises and problems regarding the basic principle of electromagnetism;

− apply the acquired knowledge on electromagnetism to different and more complex scenarios with respect to the ones explained in this course.

At the end of the course the students will be able to:

− know the fundamental electromagnetic phenomena and their laws;

− understand the most important electrostatic and magnetostatic phenomena;

− understand the electromagnetic wave propagation mechanisms in different media;

− solve exercises and problems regarding the course topics;

− apply the acquired knowledge on electrostatic and magnetostatic phenomena, and on the electromagnetic wave propagation, in different and more complex scenarios with respect to the ones explained in this course.

## Course contents summary

Introduction on electromagnetism

Review of vector algebra, differential calculus and integral calculus

Electrostatics: electric charge; Coulomb’s law and electric field; Gauss’s law; electric potential; conductors, capacitance and dielectrics; current and resistance

Magnetostatics: magnetic force; magnetic field and currents; inductance and mutual inductance; magnetic properties of materials

Electromagnetic induction

Waves

Maxwell’s equations and electromagnetic waves

Introduction on electromagnetism

Review of complex numbers and phasors, review of vector algebra and of differential operators

Maxwell’s equations

Electrostatics: charge and current distributions, Coulomb’s law, Gauss’s law, electric scalar potential, electrical properties of materials, capacitance

Magnetostatics: magnetic force, Biot-Savart law, magnetic properties of materials, inductance

Transmission lines: general properties, lumped-element model, transmission line equations, wave propagation on a transmission line, lossless transmission line, impedance matching

Plane-wave propagation: time-harmonic fields, plane-wave propagation in lossless media and in lossy media, electromagnetic power density

Introduction on radiation and antennas

## Course contents

Each class corresponds to 2 hours

CLASS 1: Introduction on electromagnetism: electric and magnetic phenomena, definition of electrostatics, magnetostatics and dynamics

CLASS 2: Review of scalars and vectors, vector operations, differential calculus, integral calculus

CLASS 3: Electric charge, Coulomb’s law, electric field, field lines

CLASS 4: Flux, Gauss’s law

CLASS 5: Electrostatic potential energy, electric potential

CLASS 6: Electric field and electric potential relation, equipotential surfaces

CLASS 7: Exercises on Coulomb’s law, electric field, Gauss’s law, electric potential

CLASS 8: Electrostatic properties of conductor and dielectric materials

CLASS 9: Capacitance and capacitors

CLASS 10: Electric charge flux, resistance, Ohm’s law

CLASS 11: Exercises on capacitance, resistance, Ohm’s law

CLASS 12: Magnetic field, force acting on a conductor, magnetic moment acting on a loop, movement of charges in electric and magnetic fields

CLASS 13: Exercises on magnetic field, magnetic force, magnetic moment

CLASS 14: Biot-Savart law, Ampere’s law, magnetic force between conductors

CLASS 15: Applications of Ampere’s law, displacement current, modified Ampere’s law

CLASS 16: Magnetic flux, Gauss’s law for magnetism

CLASS 17: Inductance and mutual inductance, magnetic properties of materials

CLASS 18: Exercises on Biot-Savart law, Ampere’s law, force between conductors

CLASS 19: Law of electromagnetic induction, electromotive force, Faraday’s law, Ampere’s law

CLASS 20: Characterization of waves, wave equation, harmonic waves

CLASS 21: Wave energy, power and intensity, typical wave phenomena

CLASS 22: Maxwell’s equations, electromagnetic waves, plane electromagnetic waves

CLASS 23: Electromagnetic wave intensity, radiation pressure, electromagnetic wave emission

CLASS 24: Exercises on waves and electromagnetic waves

Each class corresponds to 2 hours

CLASS 1: Introduction on electromagnetism: electric and magnetic phenomena, definition of electrostatics,

magnetostatics and dynamics

CLASS 2: Coulomb’s law, Biot-Savart law, electric and magnetic properties of materials (electric permittivity,

magnetic permeability, conductivity)

CLASS 3: Review of scalars and vectors, vector multiplication (simple, scalar, vector product), differential

operators in cartesian coordinates (gradient, divergence, curl, laplacian operator), divergence theorem,

Stokes’s theorem

Eletcrostatics:

CLASS 4: Maxwell’s equations (differential form, integral form), Coulomb’s law for multiple point charges

CLASS 5: Gauss’s law, electric potential, Poisson’s equation, Laplace’s equation, conductors, dielectrics,

Ohm’s law

CLASS 6: Resistance, Joule’s law, capacitance, electrostatic potential energy

CLASS 7: Exercises on Coulomb’s law, Gauss’s law, resistance, electric potential and work

Magnetostatics:

CLASS 8: Comparison with electrostatics laws, magnetic force, electromagnetic force (Lorentz force),

magnetic torque

CLASS 9: The Biot-Savart law (infinitely long wire, circular loop), magnetic force between two parallel

conductors, Gauss’s law for magnetism, Ampere’s law

CLASS 10: Magnetic field of a long wire and inside a toroidal coil, vector magnetic potential, magnetic flux

CLASS 11: Magentic field in a solenoid, self-inductance and mutual inductance, magnetic energy, magnetic

energy density

CLASS 12: Exercises on magnetic force, magnetic torque, magnetic field generated by an infinitely long wire

and by a circular loop

Transmission lines:

CLASS 13: Review on travelling waves and complex numbers, phasors

CLASS 14: Review on lumped-element circuits, impedance of two-terminal circuit elements, solution of

lumped-element circuits with phasors

CLASS 15: TEM transmission lines (coaxial line, two-wire line), lumped-element model, telegrapher’s

equations

CLASS 16: Wave equations, propagation constant and characteristic impedance of the transmission line,

general considerations on lossless transmission line

CLASS 17: Lossless transmission lines: voltage reflection coefficient (examples with matched load, opencircuit

and short-circuit), voltage and current standing waves

CLASS 18: Lossless transmission lines: minimum and maximum values of voltage and current standing waves,

standing-wave ratio, wave impedance, input impedance

CLASS 19: Special cases of lossless lines (short-cicruited line and open-circuited line, with length multiple of

half-wavelength, quarter-wavelength transformer, matched transmission line), instantaneous power

(incident, reflected), time-average power, lumped-element matching and single-stub matching

CLASS 20: Exercises on lossless transmission lines

Plane wave propagation:

CLASS 21: Faraday’s law and Ampere’s law in dynamic case, free and guided propagation of electromagnetic

waves, plane wave propagation in lossless media

CLASS 22: Electric and magnetic field of a uniform plane wave in lossless and lossy media, intrinsic impedance,

Poynting vector and electromagnetic power density of a uniform plane wave in lossless and lossy media

CLASS 23: Exercises on the uniform plane wave propagation in free space and in lossless and lossy media

CLASS 24: Introduction on radiation and antennas: antenna radiation characteristics, Friis transmission

formula, example of a satellite communication system

## Recommended readings

G. Cantatore, L. Vitale, “Gettys Fisica 2. Elettromagnetismo-Onde”, McGraw-Hill Education, 2016 (IV edizione)

Fawwaz T. Ulaby, Umberto Ravaioli, “Fundamentals of Applied Electromagnetics” (7th edition), Pearson, 2015

Fawwaz T. Ulaby, “Fondamenti di campi elettromagnetici. Teoria e applicazioni” (a cura di Stefano Selleri), McGraw-Hill Education, 2006

Fawwaz T. Ulaby, Umberto Ravaioli, “Fundamentals of Applied Electromagnetics” (7th edition), Pearson, 2015

Fawwaz T. Ulaby, “Fondamenti di campi elettromagnetici. Teoria e applicazioni” (a cura di Stefano Selleri), McGraw-Hill Education, 2006

## Teaching methods

The teaching activities include lessons carried out using multimedia presentations, videos and images (38 hours), and practice lessons (10 hours) carried out, if necessary, using software programs. Lessons are offered both “live” and online in a synchronous mode (using Teams). During the lessons, frontal teaching alternates with moments of discussion with the students. Moreover, videos of the lessons are uploaded to the Elly web-site of the course, so that students can follow them also in an asynchronous mode.

Additional teaching material used during the lessons is uploaded to the Elly web site of the course. The registration to the course is necessary to download the slides.

Students who are not attending to the course should periodically check the teaching material and the information provided by the professor on the Elly web site.

The teaching activities include lessons carried out in a lecture room, using blackboard and pc/projector to show multimedia presentations and images (36 hours). In addition, practice lessons (12 hours) carried out using blackboard or, possibly, software programs, are planned.

Additional teaching material used during the lessons is weekly uploaded to the Elly web site. The registration to the course is necessary to download the slides.

Students who are not attending to the course should periodically check the teaching material and the information provided by the professor on the Elly web site.

## Assessment methods and criteria

The learning assessment is made with a written exam, normally with exercises and some questions on the topics developed during the lessons. The aim of the written exam, which has a duration of two hours, is to verify the student’s knowledge and the ability to apply the learned concepts to problems. The written exam, during which it is allowed the use of the calculator, is evaluated in the range 0/30. The honors are assigned only for perfect tests. The mark of the written exam is normally published within a week on the Esse3 web-site.

The online registration to the exam is mandatory and it is possible until three days before the exam date.

If, in case of persistence of the health emergency, it will be necessary to do online exams, the following procedure will be adopted:

− for sessions with many registered students, written online exam using Teams. The exam will be the same as the one done in presence;

− for sessions with few registered students, oral online exam using Teams with questions and simple exercises on the topics developed during the lessons. The mark will appear in Esse3 immediately at the end of the exam session.

The instructor will inform by email all the students registered to each session about the exam type they have to do indicatively one week before the exam date. It is important to underline that the preparation required is the same for both oral and written exams.

Further information about the examination procedure will be given to the students during the lessons and made available on the Elly web-site of the course.

Students are invited to read carefully all the guides available in the section “Oral exam” of the web-site http://selma.unipr.it/ before participating to the online exams.

The learning assessment is made with a written exam, normally with exercises and some questions on the topics developed during the lessons. The aim of the written exam, which has a duration of two hours, is to verify the student’s knowledge and the ability to apply the learned concepts to problems. The written exam, during which it is allowed the use of the calculator, is evaluated in the range 0/30. The honors are assigned only for perfect tests. The mark of the written exam is normally published within a week on the Esse3 web-site.

The online registration to the exam is mandatory and it is possible until three days before the exam date.