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ECE305_exam4_soln_s04

# ECE305_exam4_soln_s04 - ECE 305 Name gob—Hons Spn’ng...

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Unformatted text preview: ECE 305 Name: gob—Hons Spn’ng 2004 Exam #4 Student No. Note: Be sure to include units and vector signs where appropriate! Note: YOU MUST SHOW YOUR WORK TO GET CREDIT! Note: Each problem is worth 8 points W 1. Faraday’s law. A conducting bar slides along conducting rails within a time- varying ﬁeld E = 52 sin(21) T as shown below. Ifthe speed of the bar is u = 10 m/s, calculate the current i(t). Assume the bar is at x = 0 at time t = 0. o z, =’Ss‘m(ax) 3 dx jag "(fit 0 ='Ss'm (27k) (15:){2‘} = -lovks'mfzt) = -!OO7‘:.\$“m {2.1“} 7.1442- ,, :3? ~ 3—“). a: ~gt(-wox S:AZ*)=+200tw323t+zeosén2>t V xitvt>= Kg): +20twsax+9O\$MZX A Maxwell’s equations. The electromagnetic ﬁelds in a source—free region of free space are given by 530,1) = 10m“: cos(3 x 10‘%— ﬂz) V/m e 1 ‘ Hf =-——‘e‘”92 A/m () my a) Find ,6 using the phasor Faraday’s law. WK?“ 2 ﬂea/Mo? V‘ : ”3 37 1% ‘géiimré ﬁg] ‘ “309/40 fi%€'3\$% 15ij (98') ﬁg .. Jwﬂoéegeﬂgé ‘ W440 _ (EXIOWHAJWMQ’?) (3’ mm ' :zmr :00 (/m H 2 continued) b) Find the time-varying Poynting vector. HCwﬂzﬂoﬂU‘igém e°W§= {€433,233 l%ws[w7t~§3) Jihad? 53); 'é mm‘ﬁmmﬁm = 207:3? ws(w;t~§g) x 7%?3 ®S(w*'135) - O " LEQ wﬂmo’oytqég) Wm?— c) Find the time-average Poynting vector. 32w (x? = g; 29% Ecmxww“? :‘éﬁeiloﬁQe’J‘53 x 712335353; :M-‘ézzi H d" é—E: g W/Mz Properties of plane waves. A plane wave of frequency 1 GHz propagates in a material with permittivity a =1680 , permeability ,u = 9 ,u() , and conductivity 0' z 0.01 S/m. Assume the material is a good dielectric at 1 GHz and that the electn'c ﬁeld is given by Em = (23? — 2 5/)e‘“ze”jﬂz a) Describe the polarization of the wave. (1)30 :7 linear Felarlzai-égm M b) Determine ,6 . w .. 54907? = zJ/urer ., W c) Determined. - 0" ,a - M91 9,41 ova—F- M1,... -; Mr N/ 2 6 Z [6290 PM 3 continued) d) Determine the phase velocity. 8 -;~_ L“ = -——-C--—- 2. w 1:. Z‘SXIO? M’s P m @(a \lﬁdé 6) Determine the wavelength. A: gr: 3—1:“ 01)ng =21§€7M (3 W i) Show that the material is a good dielectn'c at f=1 GHz. SC: 0"“ = oiouz «1, / we erxiogxigéo 4. Reﬂection of . plane waves. A plane wave is normally incident from a material with permittivity a, and permeability ,uo onto a material with permittivity so and permeability ,uz . The ﬁ'equency of the wave is 100 MHZ and the incident electric ﬁeld is E(F)=105ce“ﬂ”z V/m If the reﬂection coefﬁcient is 0.8, ﬁnd 31, and ,u2r. C) ZﬁxIDOXIOQ’ g T : w : m‘fe : M 6m 8 .. 50: E: wgg -.—:> Ear-'9 10% ”W“ l Lie 19 _ ‘- 07; '1}: Jag; ' \lgé? Jill-r 6N" § F : 0‘8: W 6" a! éxr JET-é ﬂaw: H ...
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ECE305_exam4_soln_s04 - ECE 305 Name gob—Hons Spn’ng...

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