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FinalFall2009solutions

# FinalFall2009solutions - Name 660 EE 311 Final Exam Fall...

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Unformatted text preview: Name 660/) EE 311 Final Exam Fall 2009 December 19, 2009 Closed Text and Notes 1) Be sure you have 15 pages. 2) Write only on the question sheets. Show all your work. If you need more room for a particular problem, use the reverse side of the same page. 3) Write neatly, if your writing is illegible then print. 4) The last 6 pages contain equations that may be of use to you. 5) This exam is worth 200 points. 3 (12 pts) 1.Shown are two co—centric conducting shells. The first conducting shell has inner radius a and outer radius b. The second conducting shell has inner radius c and outer radius (1. The outer surface of the outer conductor is tied to ground. The two conducting shells are initially uncharged. A point charge of +Q is placed at the center of the shells. What is the total charge in each of the following regions. Inner surface of the inner shell - Q Interior of the inner shell 0 Outer surface of the inner shell + Q Inner surface of the outer shell . Interior of the outer shell 0 Outer surface of the outer shell 0 4 C . . . (5 pts) 2. The plane 2 = 10 m carries charge 20 11—2, everywhere else 18 free space. The electric ﬁeld m 3i“ 10 9.5; intensity at the origin is, ’1‘ 4‘ f m)— V A) 4052—— m V B) —181r§z— ﬂ m A V A C) —72n a2 — A n c m D 2 'lo ’1 a m 2' -8 (— y With V( r = 00) = 0, the potential at the origin is V D ‘ yr; A) 0V \ ((0 A6) V B) <><> V I“ -———-’ C 4V Tl (lag/3677) ’ IV E) none of the above : l V 5 10*l (5 pts) 4. How much energy is stored in an arrangement of two point charges, one of charge —9—C at . to“f Am] Vlad/u) JCAr firsf (4497(9) t/‘f C B) 0.5} at (O) lMJo‘ Peiug‘r‘és no UJo/‘k. 9;; T/xe work ‘l‘o Place f/w‘ ESQ/ml, Sim/j? [‘5 (167/9) «9 (10 \$73 l0 location (0, 1m, 0) and one of charge 10‘5 C at (0, 2m, 0)? W : (03‘: ~ A T “1‘27 60 W to #4173 : l3 (5 pts) 6. A parallel—plate capacitor connected to a battery stores twice as much charge with a given dielectric as it doe with air as dielectric. The susceptibility of the dielectric is A)” a‘r dtrlmfn‘c ; £9 V " e V D)3 Q- ° 02 &Q~ér QOT. E)4 (5 pts) 7. A potential difference V is applied to a mercury column in a cylindrical container. The mercury is now poured into another cylindrical container of half the radius and the same potential difference V is applied across the ends. As a result of this change of space, the resistance is increased @l6times Volumé’ - FV‘ L, B) 8 times L‘ C) 4times R 2 E3 ....—_——- l » L. D) 2times I \‘ ST r 1 L L127!" 1 LIL. ,6 1:; R" Q 370W 67"" 6 (10 pts) 5. Derive the capacitance per unit length for the coaxial cable shown. The inner conductor has radius a, the outer conductor radius b, and free space is between the conductors. «950nm? a total elm/yr of +69 on [L'Ay‘l-Ll j 015 “f inner Conductor, have ‘5? 0A the («side 014 VA?" outer COAcoLcho/ﬂ U9CA7 G‘QUQ%\9 (aw 0" ("47' daséyJ—D Cylcf’14‘9p 2- QPAC/ .3 (Q A M e a Q 2; D“ mgr “e "‘ E aneoefl P Aqf Q A q 6) /\ 2 \/2 “Sb: M’-£méogl a? all? .9... (‘23,: ‘3» 1%le 1 ‘méoﬂ L)? “609 L) as at (Q m _ -L m»: m 9% aneuﬁ ° C t (Q Q ~ W i 7 : G - “QMOo/ay 21760.0 bats C 7 (10 pts) 8. An infinite wire is along the z-axis and carriers a current of 1A in the 5, direction. A second wire of length 1m carries a current of 1 A in the direction ﬁz direction, is parallel to the first wire and is 1 m away. (You can think of the conduction as a sliding bar of length 1 m on a rail system.) What is the force on the 1 m wire? I want a numerical value including the direction of the force. .3 .3 .3 F 2 + S I d9 2K 3 So CUP Arm} +0 +13%! lg m \m FCrgf “RAJ, H 09C“? W Amre/f‘g Law CU‘OUAJ Q'h" Ct‘chla/ fat—A 943°“) : IVE’I‘C/oSn-DQ .. A 4 H 271.6 —- I :3; H; “IA—"4‘23 o ["1 A 7 AW. " .. —- _ " ~—-- 4 : 2W0"! iii/L: S dzﬂae - 2X10 m V O 8 (5 pts) 9. In the diagram, wire one carries a current I ﬂowing out—of-the page and wire 2 carries the same current I but ﬂowing into the page. The directions of the magnetic field intensities at positions A and B, defined at the point of intersection of the dashed lines, are, mit B\\ m// mTi <D\\ m// QtT m\\ w// m—ae n\\g NM—a Eff DTT 9 C (5 pts) 10. For 2 5 0 D = 25x + 2% + 252 —2 and the relative permittivity is 8r=2. For z<0 the relative rn permittivity is 8,=4. If the z = 0 plane is a sheet charge of density 2 ——2, the electric flux m density for z < 0 is a 2: C 4"" A A c/ z A) D = 451x+4€1y +2527 m D=4ax+4ay£2 _ iML; 5—“ 3‘ - ‘* 2 ea 7 «I C) D: 151x+1€1y——2 A A. m + L/(i 5* D)D=1§x+1ﬁy+2§z£2 ; Vii" m A ,5. _ E)noneoftheab0ve DNL— DNl 2M1~O A A A Wb . . . . . (5 pts) 11. For 2 > 0 B = 23X + 23y + 2az——2— and the relative permeability 18 Mr =2 . For z<0 the relative m permeability is urzl. If the z = 0 plane is a sheet current of density 1 JAE“ the i 41tx10 m magnetic flux density for z < 0 is W B =1ax +251y +2éiz—2t3 m A A Wb B) B = 251x+1ay+2az—2 m W C) B = 4ﬁx+2§y+2ﬁz~7b m A A Wb D) B = 2§x+4ay+2az—2— m E) none of the above _ w .: W H'Ww H17 wm" 9. \ 2 l ._.» _._.'....-~ ~l 2 -\- : W“ + "ff—“:7 # l 2; HM} mxloa 3/410 “TX/D ’U" 10 (10 pts) 12. Two solenoids have the same number of turns per unit length. They have different diameters and are co—axial. Shown is a cut through the length of the two solenoids indicating the direction of current flow where the same current, 1 A, is ﬂowing in each solenoid. For the paths shown, which are in the same plane as the cut shown through the solenoid, evaluate the following integrals, 11 (6 pts) 13. Fill in the table with the standard units for the following magnetic ﬂux density, B Magnetic field intensity, H Electric Field Intensity, E Electric Flux Density, D Electric ﬂux, ‘P Magnetic ﬂux, ‘1’ (5 pts) 14. A circular loop of wire carrying current I is in a constant magnetic flux density as show. Shown is a cut through the circular 1001. “W The circular loop will A) will not rotate because the net magnetic force on a current loop in a constant magnetic field is zero. rotate clockwise C) rotate counterclockwise 12 (15 pts) 15. A 1m x 1m square loop contains a 2 S2 resistor and is moving at 1 m/s towards a region of uniform magnetic ﬁeld 10 T into the page and of width 2 m. Assume the rectangular loop begins to enter the 2 m wide region of uniform magnetic ﬁeld at t=0. Plot the current versus time in the 2 S2 resistor from t = 0 to t = 7 s. Assume the current is positive if ﬂowing in a clockwise direction. (—————-——-—-— 2m --—--———-) 7 l l l f l l l t_,~--_t.m_,,,.-___~_wJ Oététg £119 (cor) CS ENE/‘ng f/w 8"”.Ft‘vld 9.: arm (A W Kiln-twat W!» \U ‘ WE _ 1" :, V WZUtODﬁ) %\$—L((l01>-ig(’°mz ’0 L. out“ ’Flow CA 4 oeC/‘C’c‘HoA f<7 orfoc’e 'fj“ CALI‘ﬁtﬁf’ (a 4hr} Cato t/w loo/1 So 6—1712-910 '94f4 1% loop CC, (om/212+?” (FA t4: E’ﬁ‘viol. so 1» (.1 O 134 £435 t’At’ (00f Ck, [rat/047 {lusx Onto {TAP loo/9 Luci now (180'?an Same Paf'r’ it was Cmcrast‘Ag 40w 04t4l; so C: +S‘/l) the ’ooV3 C9 out of t%<" B~Hﬂd e>3§ \ so @201 dw/M;0 4nd (“:0 13 (16 pts) 16. The following is the equation of the magnetic ﬁeld intensity of an EM wave in free space. H=10cos(l .884X107t — 6.28x10‘2 2):?X A m A) What is the wavelength of the wave? ,1 A <37 31—33:: 6,}69X/0 m I / /\ 3 /00m B) What is the frequency of the wave in Hz? _, Lu a2qu = 1.88‘fX/o g" A 45:: 3X10 Ha C) What is the velocity of the wave? 7 ‘ cu / €8‘2‘X/0 S 8 Ct; “"2 ,1 _ ‘ >00 13 Q m. S A g M /\ LC - 3X/o 2—- ai D) What is the electric ﬁeld intensity of the wave? ‘J l/ I‘El :— ml Hl : (2.77 n)(xo£):377o; .3 -l , 7 A V E g .. {7709&0887‘X/ot‘618x102361ﬁ ’9 14 V (20 pts) 17. A plane wave that has Ei=50sin(6x1081tt—41ty)§x— travels in a lossless dielectric with m 81:480, 111:”.0, and impinges normally onto a lossless dielectric with 82:1680 and “2:1; 0. Determine the complete expressions for Er , Hr , Et , and Ht . - P° - W'l'ét'v‘W/M 1885.0. Ola/Z: mmww - “m iii - : 993(1). Nil/7;: Al/Ié(e.i€§erlo"“:/m) n~h 973148634 d 0.3%; [71 L * W3 Mgr-72‘ ‘ 7731+188£ A, W -W 2 +0.66'7 L ‘ 72,331, ’91314-‘83'4’ l 7&1 \ ‘ M‘ S at ~va22: (.z.w5~'§s<m<8‘“‘/X'v £3 - —-\ LU... - W : 87m 63-" UH. A "MEMO" "‘15 8 \A X» E 2 «lammlewovtﬁﬁat “x m I" i 2 A A. T = _ ww(ewowf+hmg\ dim ’ LS8.é z? fl. .. -0.08837W(6X’0W£+4ﬂ3 tr” \ A V e ,. i e 33.35%“?“0 niﬁgﬁga 47‘ m t 8 A A 15 (6 pts) 18. Material A has an index of refraction of 1.4 and material B an index of refraction of 1.1. For light in material A, the critical angle at the boundary between the two materials is A) 0° B 382° @518" D) 90° E) 180° F) none of the above ...
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FinalFall2009solutions - Name 660 EE 311 Final Exam Fall...

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