Electromagnetism I

It is difficult to overestimate the importance of Electromagnetism in the background of a physicist. It is important by itself, but also because of its influence upon other disciplines. For that reason, we understand all the mandatory modules, theory and experiment, in the Degree in Physics assigned to the Electromagnetism Area of the USC, as a compact entity. Our goal will be that by the end of all these modules, the students reach a high level of competence in this basic discipline.

We understand also that, along the Degree in Physics, there exist modules that will require a previous knowledge in the specifics of Electromagnetis. For that reason, we will try to design all our modules so they can fit in harmoniously within all the other modules of the area but also responding to the needs of the rest of mandatory modules and without overlapping with them.


Within this context Electromagnetism I, will deal with the study of the electrostatic field in vacuum and in material media, fundamentals of the theory of potential and electric current.

The general objectives of this course are:

To enhance the interest of the students by the observation, interpretation and knowledge of the physical phenomena.

Introduce the concepts and basic methods of electromagnetism necessary for the study and solution of electrostatic problems.

Learning results:

After studying the subject the student will have learned to:

Understand and handle with clarity the method and the basic principles of Electromagnetism as well as the terminology that is proper to it.

Know how to apply these theoretical knowledge to solve practical problems.

Know the interrelations between Electromagnetism with the different parts of Physics, highlighting its unifying principles.

Understand the relevance of Electromagnetism for current Science and Technology.

ELECTROSTATIC FIELD. Coulomb law. Electrostatic field. Electrostatic field divergence. Gauss's theorem. Use of Gauss's theorem to calculate fields. Curl of the electrostatic field. Helmholtz theorem. Boundary conditions.

ELECTROSTATIC POTENTIAL. Electrostatic potential. Poisson and Laplace equations. Boundary conditions for the potential. Relevant theorems. Uniqueness of potential. Calculation of the potential in very high symmetry problems. Multipolar development of potential.

CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM. Basic properties of conductors. Conductor systems. Capacitors, capacity. Force on the surface of a conductor.

POTENTIAL CALCULATION METHODS. Image method. Variables separation method. Complex variable analytical functions method.

DIELECTRIC MATERIALS. Polarization. Electric field of a polarized object. Electric displacement. Boundary conditions. Linear dielectrics.

ENERGY AND FORCES IN ELECTROSTATICS. Work and energy in electrostatics. Energy of a distribution of charges in a vacuum. Energy as a function of the fields. Energy and forces in the presence of conductors. Energy and forces in the presence of dielectrics. Pressure on the separation surface of two media. Thermodynamic considerations,

ELECTRIC CURRENT. Current density and current intensity. Continuity equation. Stationary currents. Ohmic media. Generators, electromotive force. Work and power. Non-stationary currents.

Basic and complementary bibliography




Basic bibliography:


Theory books:

- Feynman, R., Leighton, R. e Sands, M., Fisica, vol II (Electromagnetismo y Materia) (3 A00 19 A/2).
- Fraile Mora, Jesús, Electromagnetismo y circuitos eléctricos, McGraw-Hill, 4ª ed, 2005 (3 A41 97).
- Griffiths, D. J., Introduction to Electrodynamics, 4th ed, Prentice Hall, 2013, (3 A41 71).
- Griffiths, D. J., Introduction to Electrodynamics, 5th ed, Cambridge University Press, 2023, (A41 312).
- Purcell, E. M., Morin, D.J., Electricity and Magnetism, Cambridge University Press, 2013. (3 A41 129).
- Rodríguez, M., González, A., Bellver, C., Campos Electromagnéticos, 2ª ed, Ed. Universidade de Sevilla, 1999. (3 A41 61).
- Wangsness, R. L., Electromagnetic Fields, 2º ed, John Wiley and Sons, 1986. (3-A41-11A).
- Zangwill, A, Modern Electrodynamics, Cambridge University Press, 2013. (3-A41-124).

Problems books:

- Benito, E., Problemas de Campos Electromagnéticos, Ed Ac, 1976. (3 A41 47)
- López Rodríguez, Victoriano. Problemas resueltos de Electromagnetismo, Centro de Estudios Ramón Areces, 2003. (3 A41 37)
- González, A. Problemas de campos electromagnéticos, Serie Schaum, Mc Graw Hill, 2005. (3 A41 92). (Una a Good account of theory notes and problems for the same autor can be found inhttp://laplace.us.es/campos/ )
- Felisa López Cubero, Eloísa López Pérez, 100 Problemas de Electromagnetismo. Alianza, 1997. (3 A41 64).




Additional bibliography:

- Costa Quintana, Juan, Interacción electromagnética: teoría clásica, Reverté, 2007 (3 A41 101).
- Cheng, David K., Fundamentos de Electromagnetismo para ingeniería, Addison-Wesley, 1997 (3 A41 73).
- Edminister, Joseph A., Electromagnetismo, McGraw-Hill, 1996 (3 A41 49).
- López Rodríguez, Victoriano, Electromagnetismo, Uned 2012.
- Popovic, B. D. Introductory Engineering Electromagnetics, Addison-Wesley, 1973. (Libro de teoría 3 A41 98 A1, Solucionario 3 A41 98 A2).
- Reitz, J. R., Milford, F. J., Christy, R. W., Fundamentos de la teoría electromagnética, Addison-Wesley, 1996. (3 A41 20)
- Zahn, M. Teoría Electromagnética, Interamericana, 1983. (3 A41 39). A versión inglesa deste libro é de libre acceso en http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6… )



On-line resources:

- Campos Electromagnéticos, Ingeniería Industrial, Universidad de Sevilla
( http://www.esi2.us.é/DFA/CEMI/home.htm).
- K. T. McDonald's course at Princeton: (http://www.physics.princeton.edu/mcdonald/examples/#ph501).
- Physics Open Courses from MIT, in particular the different courses of Physics II: Electricity and magnetism
(http://ocw.mit.edu/OcwWeb/Physics/index.htm).
- S. Errede's course, Physics 435 UIUC: http://web.hep.uiuc.edu/home/serrede/P435/P435_Lectures.html
- S. Errede's course, Physics 436 UIUC: http://web.hep.uiuc.edu/home/serrede/P436/P436_Lectures.html
- Mark Jarrell's course, A Graduate Course on Electrodynamics LSU: http://www.phys.lsu.edu/~jarrell/COURSES/ELECTRODYNAMICS_HTML/course_EM…
- David Tong's course, Electromagnetim Cambridge: https://www.damtp.cam.ac.uk/user/tong/em.html


Electronic resources through the USC:


Through PRELO:

- Electromagnetismo I, Victoriano López Rodríguez, UNED 2013.
- Electromagnetismo II, Victoriano López Rodríguez, UNED 2016.

Electronic book:

- Introduction to Electrodynamics, David J. Griffiths, 3rd Edition 2012.

The skills that students are expected to acquire in this subject are:

Basic and general competences

CB1 - That students have demonstrated to possess and understand knowledge in an area of ;study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply knowledge coming from the vanguard of their field of study.
CB2 - That students know how to apply their knowledge to their work or vocation in a professional manner and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
CB3 - That students have the ability to gather and interpret relevant data (usually within their area of study) to make judgments that include a reflection on relevant issues of social, scientific or ethical nature.
CG1 - Possess and understand the most important concepts, methods and results of the different branches of Physics, with a historical perspective of their development.
CG2 - Have the ability to gather and interpret data, information and relevant results, obtain conclusions and issue reasoned reports on scientific, technological or other issues that require the use of knowledge of Physics.
CG3 - Apply both the theoretical and practical knowledge acquired as well as the capacity for analysis and abstraction in the definition and posing of problems and in the search for their solutions both in academic and professional contexts.

Specific competences

CE1 - Have a good understanding of the most important physical theories, locating in their logical and mathematical structure, their experimental support and the physical phenomenon that can be described through them.
CE2 - Be able to clearly handle orders of magnitude and make appropriate estimates in order to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.
CE5 - Be able to extract the essentials of a process or situation and establish a working model of the same as well as perform the required approaches in order to reduce the problem to a manageable level. He will demonstrate critical thinking to build physical models.
CE6 - Understand and master the use of mathematical and numerical methods most commonly used in Physics
CE8 - Be able to manage, search and use bibliography, as well as any source of relevant information and apply it to research and technical development of projects

Transversal Competences

CT1 - Acquire analysis and synthesis capacity.
CT2 - Have the capacity for organization and planning.
CT5 - Develop critical reasoning.

A course in the Moodle platform of the Campus Virtual will be activated. It will help to provide the students with the teaching material required to follow the contents of the course. Moreover, a work group in Teams will be created for a more efficient communication between students and teachers.


The course will be organized in 4 class hours per week in the autumn Semester. It will consist of a total of 38 descriptive classes where the contents of the program will be explained, encouraging at every time the active participation of students. Many examples will be included in those lectures. Additional problems will be solved in the interactive classes, for a total of 18 hours. The students are strongly advised to make use of the office hours, these can also take place online, but always through a previous appointment.

The final grade will be given not only by the final exam but also by intermediate assessment activities, such as solving problem's handouts or intermediate tests. The final grade of the course will be the maximum score among the following options:

a) Mark of the final exam.

b) 30% coming from intermediate activities and 70% from the final exam.


The final exam will take place in the official date fixed by the Faculty Dean Office.

The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failure in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among others, the performance of plagiarized work or work obtained from sources accessible to the public without reworking or reinterpretation and without citation of the authors and sources.

150 hours: 60 class hours (38 hours of standard classes, 18 hours of interactive classes and 4 office hours) and 90 hours of personal study

The course corresponds to a medium level Electromagnetism course. It is recommended to have previously passed General Physics I and II courses as well as all Mathematical Methods I to IV.