Electromagnetismo II - F

Ano letivo: 2011-2012
Specification sheet

Specific details
course codecycle os studiesacademic semestercredits ECTSteaching language

Learning goals

Thorough knowledge of the electromagnetic field theory, including properties of dielectric and magnetic materials, propagation of electromagnetic waves, electromagnetism relativistic formulation, delayed potentials and radiation.

Mastering of advanced techniques for the resolution of electromagnetism problems, including relevant numerical methods.


1. Electrostatics: Multipole expansion of the potential of a charge distribution. Electric dipole field and potential. Electric quadrupoles. Electrostatic energy.

2. Dielectric materials: Polarizability of a material. Clausius-Mossotti and Langevin’s Laws.

3. Laplace and Poisson’s Equations: Method of the images. General solution of Laplace’s equation in Cartesian, Cylindrical, and Spherical Coordinates.

4. Magnetic field: Magnetic energy. Magnetic multiples. Field and potential vector of a magnetic dipole.

5. Magnetism in material media: Paramagnetism and diamagnetism. Ferromagnetic materials.

Magnetization hysteresis curve.

6. Electrodynamics: Poynting vector. Poynting Theorem. The amount of electromagnetic movement. The tensor of Maxwell tensions.

7. Electromagnetic waves: Propagation in material media and conductors. Guided waves.

8. Relativity and electromagnetism: Electromagnetic tensor. Covariant form of Maxwell’s equations and continuity equation. Lorentz transformations for the electromagnetic field. Covariant expression of Lorentz’s force. Covariant equations for scalar and vector potentials. Pattern transformations.

9. Delayed potentials: the case of the isolated charges: Liénart-Wiechert’s potentials. Electromagnetic field due to accelerated charges. Radiation potency. Electric and magnetic dipolar radiation.


Electromagnetism I, Mathematical analysis III.

Generic skills to reach
. Competence in analysis and synthesis;
. Competence to solve problems;
. Critical thinking;
. Adaptability to new situations;
. Competence in applying theoretical knowledge in practice;
. Competence in oral and written communication;
. Computer Skills for the scope of the study;
. Competence for working in group;
. Competence in autonomous learning;
(by decreasing order of importance)
Teaching hours per semester
theory-practical classes30
total of teaching hours75

Problem solving25 %
Assessment Tests75 %
Exam75 %
assessment implementation in 20112012
Final exam: 100.0%
Resolution of problems + final midterm test. An alternative: 2 midterm tests throughout the semester.: 100.0%

Bibliography of reference

BRITO, L.; FIOLHAIS M. & PROVIDÊNCIA, C. (1999). Campo Electromagnético.  McGraw-Hill Portugal.

GRIFFITHS, David (1999). Introduction to Electrodynamics. Prentice-Hall.

Bibliografia complementar:

- Feynman, R., Leighton R. e Sands, M., Lectures on Physics volume II, Addison-Wesley, 1963. - - Jackson, J. D., Classical Electrodynamics, John Wiley and Sons, New York, 1975. - Lorrain, P. - Corson, D. E Lorrain, F., Electromagnetic Fields and Waves (3rd edition) Freeman and -Company, New York, 1988.

- Wangsness, R. K., Electromagnetic Fields (2nd edition), John Wiley and Sons, New York, 1979.

Teaching method

This curricular unit is extremely important for the curricular units of the following semester and for the 2nd cycle of studies. For a better learning, theoretical classes, in addition to the rigorous lecturing of the concepts, should comprise an interactive component, including many illustrations based on examples or simple experiments of demonstration.

- The use of PowerPoint presentations and computational simulations may turn the topics much more active.

- The resolution of problems, outside classes or in classes, to be corrected by the teacher, or midterm tests will help students to better follow the curricular unit’s syllabus, self-assess their own learning and contribute to their final mark.

Resources used
Uso de computadores para trabalhos de simulação computacional (resolução da equação de Laplace, traçado de linhas de campo).