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Code: EEC0012     Acronym: ELEM

Classification Keyword

Instance: 2020/2021 - 1S Ícone do Moodle

Active? Yes
Web Page: https://sigarra.up.pt/feup/pt/conteudos_adm.list?pct_pag_id=249640&pct_parametros=pv_ocorrencia_id=461242
Responsible unit: Department of Engineering Physics
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 346 Syllabus 2 - 7 70 189

Teaching Staff - Responsibilities

Teacher Responsibility
Francisco José Baptista Salzedas
Carlos Daniel Diogo Matias Pintassilgo
Mais informaçõesLast updated on 2020-09-17.

Fields changed: Teaching methods and learning activities, Fórmula de cálculo da classificação final, Melhoria de classificação, Componentes de Avaliação e Ocupação, Tipo de avaliação, URL da página, Obtenção de frequência

Teaching language



The objectives of this course unit are such that students should:

- acquire fundamental knowledge of electromagnetism;

- develop reasoning and skills in autonomous and critical problem resolution;

- acquire discipline of continued work;

- have an attitude respectful of ethical values.

Learning outcomes and competences

At the end of this unit course, student should be able to:

- correctly use the laws governing electromagnetic phenomena;

- describe electromagnetism as a unifying theory of various electromagnetic phenomena observed in nature and used in technologies;

- use appropriate technical vocabulary;

- describe practical applications of Electromagnetism;

- have a critical attitude of the obtained final results.

Working method


Pre-requirements (prior knowledge) and co-requirements (common knowledge)

It is assumed that students have:

i) knowledge of Newtonian mechanics, that is, they know the three laws of Newton and are able to describe the forces and movements they produce

ii) some basic knowledge of the atomic structure of matter;

iii) knowledge of electrical circuits, i.e., to know the laws of Ohm and Kirchhoff and know how to deal with resistors, capacitors and inductors.

iv) some knowledge about vectors (for example, add vectors, write the position-vector of a particle in three-dimensional space and compute the inner and outer product of two vectors) and elementary calculus (i.e., to derive and integrate simple functions).


1) Coordinate systems : cartesian, cylindrical and spherical; transformations between coordinate systems; elements of length, surface and volume.

2) Coulomb's Law : electric charge and its conservation; conductors and insulators ; discrete and continuous distributions of electric charge, electric force between point charges; superposition principle .

3 ) Electric Field : calculation of the electric field from Coulomb's law, the electric dipole, field lines. Gauss's law in integral form; electrical flow, the divergence theorem and the differential form of Gauss's Law .

4) Electrostatic Potential : conservative forces and fields, Stokes' theorem and the curl of the electrostatic field, the electric potential, equipotentials lines; differential relation between electric field and potential, the electric dipole, the differential form of the equations of electrostatics. The equations of Laplace and Poisson. Electrostatic energy .

5) Electrostatic of Conducting Materials : conductors in electrostatic equilibrium and theirs electrical properties , the power of the tips; electrostatic shielding.

6 ) Capacity and Electric Capacitors : plane
, cylindrical and spherical capacitors; capacitors in series and parallel; electrostatic energy stored in a capacitor .

7) Electrostatic of Dielectric Materials: polarization charge, polarization vector, electric displacement vector ;  isotropic , homogeneous and linear dielectric materials: electric susceptibility, electric permittivity, dielectric strength and dielectric rupture. Capacitors with dielectric materials. Electrostatic energy in matter. Boundary conditions of the electric field.

8) Electric Current :  current density vector. Metallic conductors : microscopic model of electric conduction , conductivity and electrical resistivity , resistivity changes with temperature. Ohm's law , electrical resistance , Joule's effect; electromotive force ; continuity equation , Kirchhoff's laws .

9) Magnetic field : magnetic force between stationary electric currents , magnetic field B , Biot - Savart law , Ampere's law in integral form , the curl of the magnetostatic field  and the differential form of Ampere's law , magnetic force on an electric charge : Newton - Lorentz equation ; magnetic force on electric currents , forces and torques in turns. Divergence of the magnetic field , the magnetic vector potential . The differential form of the equations of magnetostatics. Inductance and coils : self-induction and mutual induction coefficients, the  Neumann's formula . Magnetic energy stored in a coil.

10) Magnetic Materials : the magnetic dipole , the magnetization vector , the magnetization currents , the magnetic field H , diamagnetism , paramagnetism and ferromagnetism , the hysteretic cycle ; misotropic , homogeneous and linear agnetic materials : magnetic susceptibility , magnetic permeability , boundary conditions for the magnetic field. Magnetic circuits : the  Hopkinson's law; magnetomotive force and magnetic reluctance ; Kirchhoff's laws for magnetic circuits .

11) Electromagnetic Induction : Faraday's law of induction , Lenz's law , the alternating electric current generator , the Faraday's law of induction in integral and differential forms ; ideal electrical transformer. Magnetic energy.

12) Maxwell's equations : the displacement current , the induced magnetic field , Ampere- Maxwell's law - in integral and differential forms ; Maxwell's equations in vacuum and in the presence of matter, electromagnetic waves and the speed of light in vacuum ; plane electromagnetic waves and harmonics , the electromagnetic spectrum , the equation of conservation of electromagnetic energy and Poynting vector.

Mandatory literature

Umran S. Inan, Aziz S. Inan; Engineering electromagnetics. ISBN: 0-8053-4423-3
David J. Griffiths, Reed College; Introduction to electrodynamics. ISBN: 0-13-805326-X

Complementary Bibliography

H. Moysés Nussenzveig; Curso de física básica. ISBN: 85-212-0134-6 (vol. 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
Edward M. Purcell,David J. Morin; Electricity and Magnetism, Cambridge University Press, 2013. ISBN: 1107014026, 9781107014022
Richard Fitzpatrick; Classical Electromagnetism, 1997
Jorge Loureiro; Eletromagnetismo e Ótica, IST PRESS, 2019. ISBN: 978-989-8481-66-5
Jorge Loureiro; Exercícios de Eletromagnetismo e Ótica, IST Press, 2018. ISBN: 978-989-8481-67-2
Alfredo Barbosa Henriques, Jorge Crispim Romão; Electromagnetismo. ISBN: 972-8469-45-4
Cheng David K.; Field and wave electromagnetics. ISBN: 0-201-12819-5

Teaching methods and learning activities

Theoretical lectures (TEORICAS): complete discussion of the subjects and exercise solving of main basis cases.

Exercise classes (TEÓRICO-PRÁTICAS): exercise solving under the supervision of the teacher of several exercises.



Physical sciences > Physics > Electromagnetism

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation Weight (%)
Teste 40,00
Exame 60,00
Total: 100,00

Amount of time allocated to each course unit

Designation Time (hours)
Estudo autónomo 112,00
Frequência das aulas 77,00
Total: 189,00

Eligibility for exams

► Attendance:

-For students in 1st registration:
Number of absences defined by UP regulation.

- For students with two or more registrations:
For these students there is no criterion of attendance, ie, there is no marking of faults.

► Distributed Assessment (AD) will consist of 1 test.

-The test will be quoted in the scale from 0 to 20 values, and this is the classification to be attributed to each student.

►Students enrolling for the 1st time:

To attain admission to final exams students must:

► For other students:

Students that attained the conditions of admission to final exams in the previous academic year:

EITHER they keep previous distributed evaluation grade, where the two best marks (out of three) obtained last year are considered. For these students there is no criterion of attendance, they do not need to enroll in a class.

OR they can, irreversibly, choose to take again the distributed evaluation, being the previous distributed evaluation grade canceled. They can just attend the test.

Students that did not attained the conditions of admission to final exams in the previous academic year:

EITHER take the distributed evaluation like 1st time students

OR attend only "exame de recurso", performing this exam for 20 marks.

► Regardless of the classification obtained in the distributed evaluation, all students may attend the final exam.



► Distributed evaluation will consist of one test.

► The duration of the test is 50 minutes, involving 7 multiple choice questions and one “classic” exercise.  


Calculation formula of final grade

If the mark obtained in the exam (EX) is lower than 8.0 (minimum to be approved in the curricular unit), the final classification (CF) will be that mark. Otherwise, the final classification is given by

CF = Max (0,4*AD + 0,6*EX ; EX)


CF - Final Mark (0 to 20 points)
EX - Final Exam (0 to 20 points)
AD - Classification of the test of Distributed Evaluation (0 to 20 points).

Examinations or Special Assignments


Internship work/project


Special assessment (TE, DA, ...)

-Students who during the current school year are under special status (TE) are exempted from attendance. As mentioned above, they may obtain approval by AD or final examination.

Classification improvement

Final exam quoted for 20 values (appeal season).

Through the 2nd round Final Exam.

Final Mark will be evaluate as follows:

CF = max (CFN, 0.4 * AD + 0.6 * R, R) where

CFN is the 1st. round final grade (from 0 to 20 points), AD is the Distributed Evaluation grade (from 0 to 20 points) and R is the 2nd. round Final Exam ("Exame de Época de Recurso") grade (from 0 to 20 points).


-Students should dedicate to the study of the curricular unit about 5 hours per week, in addition to the usual frequency of classes.

-Any attempted FRAUD during the distributed evaluation process leads to loss of frequency and not admission to examination.

-Weekly attendance to students is accomplished through a direct negociation between the student and the professor.
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