329sp08he2sol

329sp08he2sol - ECE 329 Introduction to Electromagnetic...

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Unformatted text preview: ECE 329 Introduction to Electromagnetic Fields Spring 08 University of Illinois Goddard, Peck, Waldrop, Kudeki Exam 2 Thursday, March 13, 2008 — 7 zoo-8:15 PM Name: . b m l 9 AM 12 Noon 1 PM 2 PM Please clearly PRINT your name in CAPITAL LETTERS and circle your section in the above boxes. This is a closed book exam and calculators are not allowed. You are allowed one formula sheet of 8.5 by 11 inch dimensions — both sides of the sheet may be used. Please show all your work and make sure to include your reasoning for each answer. All answers should include units wherever appropriate. TOTAL (100 points) 1. Consider plane electromagnetic wave propagation in free space. Magnetic field intensity of the wave is given as H = y2cos(37r~108t — ,Bz) m a) (4 pts) Given that the wave is known to propagate in +2 direction what is the numerical value of ,8 (stated with proper units)? W‘C a) fi,%: ‘3qu03 =fi'fl/ 7;” me‘ M b) (3 pts) What is the corresponding wavelength? A=gzflT=ZM~. e Tr / c) (7 pts) What is the expression for the accompanying wave electric field E (with proper units)? A A Y N‘ “I: ‘7 E = [62.0130 £1740 4,-— (42-) .E; ) 41.2mm, > x 5.5 fizuou'mBW-to‘b—{az} V/Wfl. "’E d) (7 pts) What is the instantaneous Poynting vector at t = fig s on 2 = é— m plane? I i , .. 1 P: BxH =€4fiofiwt (31“0't-(5?)L =€4ioflm‘(zw-g)=0/ ii. z = 1 m plane? ‘(3 3 4; 4eomaf(2fi - fl) = 3 “y e) (4 pts) In view of energy conservation and the results of part (d), determine if energy is being stored into or released from the electromagnetic field at t = 5% s within a cube of % m dimensions located between 2 = % m and 2 = 1 m planes? Briefly state your reasoning. am?” if Mimaai af‘hwq' {ash-.1 beacon—c. - Wei Mule—rt! Fowu 2. (25 pts) A right-circular polarized electromagnetic wave with a co—sinusoidal time variation and a frequency of w = 67r - 108 rad/s is propagating in +z direction in free space. What is the expression for the wave electric field E(z,t) given in the time—domain if it is known that E(0,0) = 45; V/m? Your answer should include a brief but detailed explanation of how your expression for E(z, t) agrees with the wave description given above. {5: w‘zén‘xwlzafi Z 1;? " A . A ' é . “c-ZIr v E : 47 an(£fl 4031;. 2H2) + 4.3 9;».(1? m a) I” WWW.WmWMHy.a.«.weWW.trNW4W.WeWmwemum“.Wimmflwwmwwmmwmawummmwwm.w.mmm A ‘ 11H, .. ZIT-E'eJ ‘ 2 g “a! 0 ‘7 ‘0 ‘" —) H ’?J9i:wm(zn-lo‘{+2n%-_r_r)fi (a m, 69)!qu 4% ‘t In . >X 3. A plane wave with an electric field waveform 2’. 9 I 6MB}! 4 D E : ~1062“ cos(27r - 10775 + 27rz):% X (“7 E 3 m is observed to propagate in some material medium with ,u = 10w, Where ,uo = 471' - 10—7 H/m. 1 E i E W i i a) (3 pts) Express the phase velocity of the wave as a vector pointing in the propagation direction. i i i i l i q. % U:21T'l01') S9=2Tr ‘5) U}=‘é-;:l° “4/; E % A "i‘ - ‘ i .1 F :: azlo m/S 7N... ma Tutu/owns tame/(Am; % P c... — '5 awed)“ 5 b) (4 pts) Find the propagation constant 7, expressing it in exponential form in terms of magnitude E " M and phase. , % l E 3 i E E E l E 3 Tl "‘ r.) m: 24% a; t , J 7;: x45}..— Z-a +-J an = 217043) arr/h! e, Ab]: J}; Y“- c) (6 pts) Find the complex impedance n in terms of magnitude |77| and phase ’7‘. Hint: 777 = jw/r. -;a’.[o"'.|o.po , o{.4nxla1 ,- .fi .1 Cf) /’* __. Kiowa-t) /‘4 'w (4 _ yer; eJ 41“ W '5 - t M144 MI (1) (8 pts) What is the associated magnetic field waveform H? A :5 (o e) (4 pts) Explain Whether the material should be considered a perfect dielectric, imperfect dielec- tric, good conductor, perfect conductor, or none of these. W Undudv/ lh-CMR o(={i. 4. An infinite dielectric slab with a finite thickness W in z direction has a uniform DC polarization of P = 22 C/m2 when the electric field outside the slab due to external charges is known to be E0 = $2 V/m. The slab is embedded in free space with permittivity an m mg F/m. M“ ’T : M e l ED3 2050 A a) (7 pts) What is D inside the dielectric slab? Explain your reasoning. 33:43 git - Pram; fro. In. flak- b) (8 pts) What is the electric field vector E Within the dielectric slab? ’. “— —- " fl _' 32' a D:‘E.F+P —> 5—D P :42 2%, ._% 33% F $9 in 2° c) (5 pts) What is the electric susceptibility Xe of the dielectric if P is known to be linearly related to E via the relation P = eoer? GEL-oneg =7 l‘xe, 3) (2% “E? d) (5 pts) What is the permittivity e of the slab in terms of so? 2: 21mg) = aim) = 22%. ...
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329sp08he2sol - ECE 329 Introduction to Electromagnetic...

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