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Code: EEC0012     Acronym: ELEM

Classification Keyword

Instance: 2011/2012 - 1S

Active? Yes
Web Page: https://www.fe.up.pt/si/conteudos_adm.conteudos_list?pct_pag_id=1639&pct_parametros=p_ano_lectivo=2011/2012-y-p_cad_codigo=EEC0012-y-p_periodo=1S
Responsible unit: Department of Physics Engineering
Course/CS Responsible: Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEEC 443 Syllabus (Transition) since 2010/2011 2 - 7 77 189
Syllabus 2 - 7 77 189

Teaching language



The objectives of this course unit are such that students may acquire basic knowledges of Electromagnetism
(an underlying science of Electrical Engineering) and that students may develop their own personal and professional skills and attributes.

At the end of this course unit students are exepcted to have acquired the following skills.

1. Technical Knowledge and Reasoning (CDIO 1.1,1.2)
- To apply correctly the laws which rule the electromagnetic phenomena.
- To present Electromagnetism as an unified model of the different electromagnetic phenomena observed in Nature and used in Technology.
- To use the proper technical terminology in order to explain the different electromagnetic concepts and phenomena.
- To describe and explain some of the basic applications of Electromagnetism, such as, capacitors, resistors, coils, electric motors, electric generators, electric transformers, semiconductors, diodes, magnetic circuits.

2. Personal and Professional Skills and Attributes (CDIO 2.1,2.3,2.4,2.5)
- To enumerate Pólya's Four Steps and through these to acquire skills in order to solve critically and autonomously exercises about the course subjects.
- To develop a critical attitude towards the final result, namely, using dimensional analysis, estimative of the expected order of magnitude, interplay between the different quantities and solution's behaviour in specific limit cases.
- To acquire the discipline to work continuously during the semestre.
- To attain skills concerning written communication.
- To develop an attitude respecting ethical values such as mutual respect, responsibility and honesty.

3. Interpersonal Skills (CDIO 3.1,3.2)
- To acquire skills concerning teamwork.
- To attain skills concerning oral communication.


1) The cartesian, cylindrical and spherical coordinate system; transformations between systems; differentials of lengths, surface and volume.

2) Coulomb’s Law: electric charge; electric force; conductors and insulators; superposition principle.

3) The electric field; fileds lines; electric flux and Gauss’s Law; applications of Gauss’s Law; the divergence of a vector field and Poisson’s equation.

4) The electrostatic potential: conservative fields; electrostatic potential; examples of electrostatic potential calculations; electric dipoles; the rotational of the electric field; the local form of the electrostatic equations; electrostatic energy.

5) Electrostatic capacity and capacitors: method of computation of the capacity of a capacitor; examples; capacitors in series and parallel; electrostatic energy in a capacitor.

6) Electrostatic of conducting and dieletric materials: electrostatics of conductors; polarization of dielectrics: polarization charges and the electric displacement vector; linear dielectrics; boundary conditions; elctrostatic energy in matter.

7) The electric current; definition; charge conservation; continuity equation; Ohm’s law and conductivity; the kinetic model for Ohm’s law; wave properties of electrons; the band spectra (conductors; insulators and semi-conductors); Joule effect; electromotive force; Kirchhoff’s laws.

8) The magnetic field: the magnetic force between currents; Ampère’s law and its applications; the Biot-Savart law and it’s applications; the Lorentz law; the Hall effect.

9) Electromagnetic induction: Faraday's law of induction and Lenz’s law; electric generators and motors; mutual and self inductance; magnetic energy.

10) Magnetic materials: magnetization currents; the H field; diamagnetism; paramagnetism and ferromagnetism; boundary conditions for the magnetic field; magnetic circuits; the ideal transformer.

11) Maxwell’s Equations: a summary of what one has learnt so far; the displacement current; plane electromagnetic waves; energy balance and Poynting’s vector.

Mandatory literature

Alfredo Barbosa Henriques, Jorge Crispim Romão; Electromagnetismo. ISBN: 972-8469-45-4

Complementary Bibliography

H. Moysés Nussenzveig; Curso de física básica. ISBN: 85-212-0134-6 (vol. 3)
David J. Griffiths, Reed College; Introduction to electrodynamics. ISBN: 0-13-805326-X
Umran S. Inan, Aziz S. Inan; Engineering electromagnetics. ISBN: 0-8053-4423-3
Daniel Fleisch; A student.s guide to Maxwell.s Equations. ISBN: 978-0-521-70147-1
Daniel Fleisch; A Student's Guide to Vectors and Tensors, Cambridge University Press, 2011. ISBN: 0521171903

Teaching methods and learning activities

Lectures: theorical classes where the underlying concepts of the course unit are introduced and illustrated with examples and applications.

Recitations: exercise classes where students solve exercises under the supervision of the teacher.

Moodle site: download of theoretical lectures presentations, multimedia resources, exercises sheets, self-evaluation tests, general information on the course, presentation of midterm-exams and exams results.

Office hours: personalized tutorship where doubts on the theory and exercises are clarified.


Physical sciences > Physics > Electromagnetism

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description Type Time (hours) Weight (%) End date
Attendance (estimated) Participação presencial 70,00
Exame 1,50
Exame 2,50
Total: - 0,00

Amount of time allocated to each course unit

Description Type Time (hours) End date
Estudo autónomo 78
Estudo autónomo 12
Estudo autónomo 25
Total: 115,00

Eligibility for exams

To attain admission to final exams students must:
- not exceed 3 absences to exercise classes.
- get a minimum grade of 7 (out of 20) in the distributed evaluation.

Distributed evaluation is performed by 1 midterm exam. The midterm exam will consist of one exercise (10 points) and ten multiple choice questions (4 points). Midterm exam will last 1h:30 minutes and will be performed at a date to be announced.

Students that attained the conditions of admission to final exams in the previous academic year are dismissed from attending classes, being the previous distributed evaluation grade kept. Nonetheless, these students can choose to enroll on one exercise class and to be submitted to the distributed evaluation, being the previous distributed evaluation grade canceled. This option is irreversible.

Please see also Article 4th of "Normas Gerais de Avaliação da FEUP".

Calculation formula of final grade

AD - Distributed Evaluation (0 to 20 points)
EF - Final Exam (0 to 20 points)
CF - Final Mark (0 to 20 points)

If AD >= 7 then the student is admitted to final exams.

In order to pass the course (final mark CF >= 10 points) students must get a minimum of 8 points on the final exam.
Distributed Evaluation has a 40% weight and Final Exam a 60% weight.

If EF >= 8 then CF = MAX (EF ; 0.4 * AD + 0.6 * EF)
else CF= EF

Examinations or Special Assignments


Special assessment (TE, DA, ...)

- Students that have a special status (working students,military students) during the present academic year are dismissed from attending the classes and therefore to get a distributed evaluation grade. For these students the final mark will be that of the final exam. Nonetheless, these students can choose to enroll on one class and submit to the distributed evaluation. This option is irreversible.

- Please see also Articles 4th and 6th of "Normas Gerais de Avaliação da FEUP".

Classification improvement

Through the 2nd round Final Exam.

Final Mark will be evaluate as follows:

CF = max (0.4 * AD + 0.6 * EFN, 0.4 * AD + 0.6 * EFR, EFR)

where CF is the Final Mark (from 0 to 20 points), EFN is the 1st. round Final Exam ("Exame de Época Normal) grade (from 0 to 20 points), AD is the Distributed Evaluation grade (from 0 to 20 points) and EFR is the 2nd. round Final Exam ("Exame de Época de Recurso") grade (from 0 to 20 points).


- Weekly time of study, beyond classes, is expected to be around 6 hours.

- Informations and support material are available at moodle web page of the course: http://moodle.fe.up.pt/0809/course/view.php?id=169

- At the end of the course unit students are exepcted to have acquired the demanding skills to use without any difficulty the textbook "A Student's Guide to Maxwell's Equations" of Daniel Fleisch (see bibliography).

- Any attempt of FRAUD during the distributed evaluation corresponds to fail immediately the course.
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