Electrodynamics II 7.5 credits

About the course

Content The course begins with a brief repetition of basic concepts such as Poynting's theorem, potentials and gauges transformations, and then the retarded and advanced potentials are derived. Then special relativity theory is treated in 4-vector form, and electrodynamics are formulated in covariant form. Lagrange and Hamilton methods in field theory are then introduced. Energy momentum tensors are introduced and various conservation laws are derived. A large part of the course is devoted to radiation theory. First, multipole radiation with emphasis on dipole and quadrupole radiation is treated. Radiation from accelerated charges is then studied and the Lienart-Wiechert potentials are derived. Further, the frequency spectrum of the synchrotron radiation and the theory of radiation attenuation are discussed. As an application, some different examples of antennas are studied. The course also contains something about special functions, such as spherical harmonics and Bessel functions, as well as the theory of Green's functions.

Expected study results To fulfil the goals of knowledge and understanding, the student should be able to: - explain in detail key elements such as retarded potentials, special theory of relativity, electrodynamics in covariant form and Lagrange methods in classical field theories - provide in-depth description of radiation theory, including multipole radiation, accelerated charge radiation, frequency spectrum and radiation attenuation - derive central results in electrodynamics and explain in depth these arguments.

In order to fulfil the goals for proficiency and ability, the student should be able to: - independently perform advanced calculations in electrodynamics eg. of radiation fields and power from different current and charge distributions - independently apply electrodynamics to e.g. determine the radiation from different antenna designs - systematically determine the radiation field and power from accelerated charges, the frequency spectrum of the radiation and the radiation attenuation for charges - derive field equations (or equations of motion) from a Lagrange description of a relativistic theory, determine the corresponding energy-momentum tensor and derive conservation laws from this.

In order to fulfil the goals for values and critical approach, the student should be able to: - independently and with a critical approach, make use of scientific literature in the field.

Forms of instruction The teaching is conducted in the form of lectures and problem solving sessions.

Examination The examination for the course's theoretical part takes place individually in the form of a written exam at the end of the course and voluntary hand-in problems. For the written examinations one of the grades Fail (U), Pass (G) or Pass with Distinction (VG) is set. The points awarded for the hand-in problems can be reused at a later re-exam. The course grade will be the same as that of the written exam (including the score from the hand-in problems). A student that have passed the exam can not take another exam in order to get a higher grade.

Literature Jackson John David Classical electrodynamics 3. ed. : New York : Wiley : cop. 1999 : xxi, 808 p. : ISBN: 0-471-30932-X

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Autumn 2025
- Electrodynamics II
  
  Second admissions round for EU/EEA citizens
  
  Autumn 2025 / Umeå / English / On site
  
  Submit a late application
  
  Show more Show less
  
  Starts
  3 November 2025
  
  Ends
  18 January 2026
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-53008
  
  Eligibility 90 credits including Analytical Mechanics and Electrodynamics or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies. Requirements for Swedish only apply if the course is held in Swedish.
  
  Selection
  Academic credits
  
  Application
  Application deadline was 15 April 2025. Please note: This second application round is intended only for EU/EEA/Swiss citizens. Submit a late application at Universityadmissions.se.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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