# 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 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 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: 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

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 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.