# 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.

## 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

## 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 (gradient, divergence, curl, laplacian operator), 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

## 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

## Teaching methods

The teaching activities include lessons carried out in a lecture room, using blackboard and pc/projector to show multimedia presentations and images (38 hours). In addition, practice lessons (10 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.