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# Electrodynamics II

• 7.5 credits
• Master’s level
• Autumn Term 2023

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
• 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

## Application and eligibility

### Electrodynamics II, 7.5 credits

Autumn Term 2023

31 October 2023

14 January 2024

Umeå

English

Daytime, 50%

#### Required Knowledge

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 Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

UMU-53024

#### Application

Application deadline was 17 April 2023. The application period is closed.

#### 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.

SEK 900

SEK 17,850

SEK 17,850