The aim is to familiarize the student with the most common applications of Maxwell's equations in the following fields: problems in static fields, propagation of electromagnetic waves, generation of electromagnetic radiation, microscopic theory of electromagnetic effects on material, and transformation of the electromagnetic field between inertial frames (special relativity). This subject is compulsory in the 3rd year both for students of the Degree in Physics, Degree in Electronic Engineering and double degree in Physics and Electronic Engineering.



To follow this course, it is necessary to have the following prior knowledge: knowledge of electromagnetic phenomena that are included in Maxwell's equations, differential equations, resolution of boundary problems, propagation of mechanical waves and knowledge of the atomic structure of matter. This knowledge has been acquired during the second year of the degrees in Physics, Electronic Engineering and double Degree in Physics and Electronic Engineering in the subjects of Electromagnetism I, Mechanics I and Structure of Matter.

The COMPETENCIES that will be worked on this course are:

- Getting to know the necessary knowledge to clearly understand the basic principles of Electromagnetism and its applications.

- Correctly proposing and applying the appropriate techniques to solve problems that involve the main concepts of Electromagnetism and its applications.

-Communicating, both orally and in writing, knowledge, problems and questions about Electromagnetism to develop skills in scientific communication.



The learning RESULTS for this subject, that is, the specific knowledge and skills that students must acquire throughout the course are the following:

- Solving electrostatic and magnetostatic problems in two dimensions by separating variables and the image method.

- Knowledge of the propagation laws of the electromagnetic field in dielectrics and conductors and in the separation surface between them.

- Solving EM field propagation problems in simple rectangular wave guides. Knowledge of the properties of rectangular resonant cavities and obtaining the resonance conditions.

- Knowledge of the fundamentals of EM wave radiation by moving charges, and in particular the dipole radiation. Application to radiation by antennas and by atoms.

- Knowledge of the microscopic mechanisms of polarization, electrical conduction and magnetization in matter, and the macroscopic equations that describe it. Solving simple problems of electrical and magnetic properties of matter.

- Knowledge of the transformation properties of charges and currents, potentials and fields in a change of reference system (relativistic formulation of EM) and resolution of simple field and potential transformation problems.

Electromagnetism II (6 ECTS, mandatory, 3rd Course of the Degrees in Physics, Electronic Engineering and Double Degree F-IE))



Program:



1.- Problems of boundary conditions for static fields: Maxwell's equations in a vacuum and in continuous media. The Poisson and Laplace equations. Solutions of Laplace's equation in two dimensions. The method of images. Boundary conditions problems in magnetostatics. Introduction to numerical methods.



2.- Electromagnetic waves in unlimited media: Monochromatic plane waves in dielectrics. Polarization. Energy and momentum of EM waves. Waves in conductors: complex refractive index, skin effect.



3.- Electromagnetic waves in limited media: Reflection and refraction of EM waves. Fresnel formulas. Guided wave propagation: rectangular waveguides, cut-off frequency. resonant cavities.



4.- Radiation of electromagnetic waves: Delayed potentials: quasi-stationary and radiation regimes. Electric dipole radiation. Magnetic dipole radiation. antennae.



5.- Electromagnetic Theory of matter: Microscopic theory of dielectrics. Dependence of the permittivity with the frequency, dispersion. Microscopic theory of Magnetism. Conduction in solids, superconductors.



6.- Relativity and Electromagnetism: Lorentz transformation, quadri-vectors and tensors. The electromagnetic field tensor and Maxwell's equations in covariant form. Transformation of the electromagnetic field.

ECTS credits: 6 (150 hours: 60 face-to-face teaching hours and 90 student working hours)



A combination of teaching methods is used including:



- For the development of theoretical content, master classes that are complemented by classrooms exclusively dedicated to problem solving.



- For the development of continuous assessment, self-assessment tests will be proposed throughout the course.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 100

CONTINUOUS EVALUATION



There will be 2 partial exams (3 topics in each one):

- They will be done during teaching hours.

- The student must pass the first written test exam with a grade >=4 to be able to participate at the second partial exam.

NOTE: to pass the course, an average grade >=5 is mandatory.



Self-assessment tests will be carried out throughout the course.



Final mark of the course EM-II:

Grade = Average grade from partial exams + 0.15 x Grade for tests

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FINAL EVALUATION



If the student does not pass or failure to take the partial exams, the course will be graded through the Final Exam.



Final mark of the course EM-II: Final Exam mark (ordinary examination period)

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OPTING OUT



Failure to take the test set on the official exam date will automatically waive the corresponding call.

The same criterion of the FINAL EVALUATION in ordinary examination period is maintained, that is, the grade for the subject will be the mark of the exam carried out in the extraordinary call.



-------------------------------------

OPTING OUT



Failure to take the test set on the official exam date will automatically waive the corresponding call.

Notes and problems of the subject (eGela webpage of the course: https://egela.ehu.es)

Basic bibliography

1) J.R. Reitz y, F.J. Milford y R.W. Christy, FUNDAMENTOS DE LA TEORIA ELECTROMAGNETICA, Addison-Wesley Iberoamericana, Delaware (1996).



2) P. Lorrain y D.R. Corson, CAMPOS Y ONDAS ELECTROMAGNETICOS, Selecciones Científicas, Madrid (1979).



3) D.J. Griffiths, INTRODUCTION TO ELECTRODYNAMICS, Prentice-Hall Inc. USA-1999.



4) R.K. Wagness, CAMPOS ELECTROMAGNETICOS, Limusa, México DF (1983).



5) M.A. Plonus, ELECTROMAGNETISMO APLICADO, Reverté, Barcelona (1982).

In-depth bibliography

6) J.D. Jackson. CLASSICAL ELECTRODYNAMICS. 3ª ed., Wiley, 1999

Other helpful bibliography:

7) MANUAL DE MATEMATICAS, I. Bronshtein y K. Semendiaev, Ed. Rubiños, Madrid (1993).

Journals

Revista Española de Física

Web addresses

http://www.sc.ehu.es/sbweb/ocw-fisica/elecmagnet/elecmagnet.xhtml
http://academicearth.org/courses/physics-ii-electricity-and-magnetism
http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/CourseHome/