EFWA 09 Test 1

Student namc:

Fields, Wave* & Antennas: Tw*t J. 2 April 2009

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>    Botd letters dcnotc vcct«>rs.

>    Italie* dcnotc sesłar variahlcs.

>    Bold italle* dcnotc \ector variahles

'f Plcase specify iiitlts in all jotir answers'

>    Intrinsic impcdancc of yaaturn ¹ 120 n Q; 3* 10^ m/s. r Maximuni nnmber of points for cach problem: 6.

Probiera I:

Given a magnetic field:

H » I, Ho cosj ni/-:/ v)J i. Hu sini oĄt - z i v)] |A/mJ

determine the elcctric field £ in losslcss non-magnetic didectric of £>=9, using the Maxwell equatinn<t    M

piane wave propert ics!).

Find a retation between v and medium parameters.

Problem 2:

Consider an anisotropic medium with permcability given by a diagonal tensor, fi_x^m 1, //,=4, fi.=I. Calculate the magnetic llcld H and an angle between H and B fields if B - i_y B₀ +i,B₀

Problem 3:

Consider a homogeneous isotropic lossless medium. Can the following static magnetic field be generated in dus medium: /#(/, r) ~ //<, (i* siny + i_y siar) {A/mj? By what means? Justify your answer by considering appropriatc Maxwełl equations.

Problem 4:

Calculate flux of vector .4 - i,.v + t_r.r + i, (,v+2) through the surface of a cube with sidc </“2 and ceatrc at the origin of the coordinatc system. Use two methods: direct surface integration and Gauss theorem.

Problem 5:

Whioh cxpression(s) can describe electric field of a single piane wave (ar a superposition of several piane w*ves) travelling in a homogeneous isotropic medium without sources? Assume e=Eo and consider two cases regarding losses: land =0 and land =1.

a)    £(l, r) = i, £o sin(tuf) sin (/i r).

b) E(r. r) * Isinfa* - fi, x)-i_x £> sinftur - fi.2)

c) £(/, r) = i, £0sin(ox - fi,.t) -1, £1 sin(<ar - fi, x)

where £>. fi,, fi. - real numbers; fi, >0. fi->0. Justify your answers. Use piane wave properties to calculate the magnetic field. Specify relations between a;and fi,, fi-..