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JI J

ELT-41736 Analysis of Electromagnetic Systems
Small Exam II 02.12.2013

Answer to all guestions.

Jari Kangas

JE

2.

3.

(6 p. in total)

(a) Describe the laws that govern magnetostatics in free space. Define also briefly the
guantities used.

(b) How are the laws changed if we consider domain that is not free space? (Aim to give
detailed answer, i.e., complete set of conditions inherent in the case.)

(c) In the electrostatic case we introduced so called electric scalar potential. Could we
se in magnetostatics scalar potential? If yes/no, try to give a thorough reasoning.

 

(a) In electromagnetic motors, for instance, so called laminated structures are used (see
the black board).

i. Explain in which kind of cases such structures are needed. Reason why such
structures are useful, use suitable EM laws to support your reasoning.

ii. Reason also suitable direction of the lamination with respect to relevant EM
guantities.

(b) Show that if F(r) = Acf*" (where A is constant vector and J? =-1),
V-F=jk-Fandd V xF=jkxF.

(5 p. in total)

(a) Consider'solution to an electromagnetic wave problem. Let us suppose two candidates
for electric flux density Di and D2 for which holds that V - (D1 — D2) = 0. Does
this mean that D1 = D2? If no, how are they related to each other?

(b) In certain cases electric potential due to charges is given as
rr")

(2/4
dlr, 1) = 1 ju ST AW".

Explain what is special in this expression and how to interpret it. Consider also
fundamental assumptions underlying in basic circuit analysis; how could you relate
the intepretation to them.

(4 p. in total)