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FinalFall2010solutions

# FinalFall2010solutions - Name 30 l Q £6011 EE 311 Final...

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Unformatted text preview: Name 30 l Q £6011 EE 311 Final Exam Fall 2010 December 16, 2010 Closed Text and Notes, No calculators 1) Be sure you have 13 pages and the additional pages of equations. 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. 5) This exam is worth 150 points. 3 (5 pts) 1. A point charge of 30 nC is located at (—1, 0, 2), —20 nC at (0,0,0) and 10 nC at (1,5, —l) The total electric flux leaving a cube of side 6 centered at the origin is A) — 20 nC D) 30 HC 10 nC E) 60 nC C) 20 nC (20 pts) 2. Circle true or false concerning the statements for a ferromagnetic material. The electric ﬂux density on a spherical surface r = b is the same for a @ False point charge Q located at the origin and for charge Q uniformly distributed on surface r = a where a < b. - True The inductance of a coil is independent of the current flowing through @ False the coil. A ferromagnetic material retains a considerable amount of its magnetization when removed from an externally applied field. Electric flux lines are never closed. False Two thin parallel wires carry currents along the same direction. The False force experienced by one due to the other is perpendicular to the wires WIIIEII and attractive. an @1 the net power flowing out of that surface. A standing wave occurs when the electric and magnetic fields of a TEM wave are out—of—phase. The critical angle is where the angle of incidence equals the angle of reﬂectance. (5 pts) 3. A 5 MC point charge is located at (1, 7t/4, n/2) and experiences a force of F=10§r —559 +25% N. What is the electric field intensity at point (1,7t/4,1t/2)? ,3 e- (IOQP’SQB +1929)” l..- Et‘MZP—‘T/ C? S‘X/p‘C 6 N .. (air—ja+§dﬁp)X/O Z— 4 A A E :(Qar‘dg+5g¢)X/O M (5 pts) 4. There is a 1 HC point charge at (—1 , 1, 0), a 2 nC charge at (0,0, 0), and a l nC point charge at (1,1,0).Choose V( r =°°)=Oand use 80 in the form 80:22; E in your calculations. m V(0,1,0)is V— ,‘7 9 A)0V B)<><>V C)4V D)1V 2 . “men L -6) -a @3‘” ‘ .5‘7c 2x106 10 C F)18V ~ ____.,_c—'-—-;_: ———--'‘\-——--“"‘\"""'l ’ - - A m G)9V “UT/‘0 7; {M \m 36W H) none of the above 5 (8 pts) 5. For the currents and closed paths shown in the following four figures, evaluate qu odl é it) A 10 A Q “W'J/ ‘3 30" (h) (a) gliH-dbloﬁ ﬁnal] {20?} din-<11: O din-an: 409 (5 pts) 6. Which of the following statements is correct? a)“ The magnetic flux density is due to free and bound currents, the magnetic field intensity is due to free currents, and the magnetization is due to bound currents. b) The magnetic ﬂux density is due to free currents, the magnetic field intensity is due to free and bound currents, and the magnetization is due to bound currents. c) The magnetic flux density is due to bound currents, the magnetic field intensity is due to free currents, and the magnetization is due to free and bound currents. d) The magnetic ﬂux density is due to free currents, the magnetic field intensity is due to bound currents, and the magnetization is due to free and bound currents. 6 (10 pts) 7. Two identical spherical conductors of radius a = 1m are brought into contact at a single point P. A total charge of Q = —1 nC is placed on the conductors such that the potentials for the two conductors become VI and V2 . 1,. /, \\ \._ (3 Pts) a) What is the relationship between V1 and V2? / _ Conalod'ol‘g a/‘r QZUCfofP/xﬁ‘a é. §LM70 A KAeSQ two COAAUC are a”? CA C‘bAi’W—f, t fly 6H“? 41‘ {Av Sam? FO‘iW/Vi's‘tcl Vtzv 9x (2 Pts) b) Find the electric field inside the two contacting spheres. There C3 A0 c/xa rj-e {ActJ <9 “(4:99? (vol-oct-ol‘é) go {Ar/r is II o P {:0 dTL L \$36160 @934? E :0 (5 pts) 0) Find the total electric ﬁeld at (s, y, z) = (o, 0, 10 km). Hint, take advantage of 10 km >>> I m 10‘9 F and Use 80 in the form 80 = — in your calculations. 36TI: m From [0 km awa/l me? SPAQ‘es ouCl/ Asok like 4 P03” CAdv‘j? 61(‘ “(AC all ﬁle arty/L l C) A ‘ "10m,C A 7 (15 pts) 8. A parallel plate capacitor has plate area 0.5 m2 , plate separation 0.02 m, and a dielectric between the plates of relative permittivity 8r = 4. A battery is connected to charge the positive plate with 8.854x10'9C and the negative plate with —8.854x10‘9C . The plates are parallel to the yz plane and the positive plate is at x = O and the negative plate at x = 0.02 m. F Ignore ﬁeld fringing at the edges of the capacitor and 80 = 8.854X10—12 — . m (5 Pts) a) What is the electric flux density inside the capacitor? 6) 8 85 '1 2g, ‘ 9 Q ~ 9 c. - . 2. .. ' 0 D - es 7 ~ :: |'7.'7o}?XIo ’1' 0. S M ‘- m .3 “1°C A (5 Pts) b) What is the electric ﬁeld intensity inside the capacitor? 4 E Q E __ I7.708)</6qf; 7(_ '033 __§__ ere» (Magma); W (5 Pts) c) What is the voltage drop across the capacitor v =- EGQ =(5005: (mow/o 2 IO \/ 8 A (12 pts) 9 The z = 1 plane contains a sheet current density of K = 10 — ﬂy. The z = —1 plane contains a m A A . . sheet current density of K = 10 — ay . Find the magnetic ﬁeld Intensny everywhere. In 2— g 9 (10 pts) 10. A 1 kg sliding bar is on the rail system shown. The magnetic ﬂux density is everywhere 13:15z T, If the bar starts at rest at x = 0, what isthe force on the sliding bar? Assume the resistances of the rails and the sliding bar are negligible. 10 (12 pts) 11. Consider the following conducting loops placed in the indicated magnetic ﬁelds. If current is ﬂowing in the direction of the arrow, clockwise, the current is considered positive. Indicate whether the actual current ﬂowing is positive, negative, or zero for the indicated conditions. Note the positive y-axis is into the page. B=Boﬁy B=B0tfly ® ® ® ® ® ® ,7 ~_\ A-:§\ / \ / \ ® \ ® , ® ® \ ® ; ® “\_ \\ / ® ® ® ® ® ® \- Its iel‘o lis n%mfu/‘P z B=Boﬁy B=Botay T w. Ag, X ® ® ® ® ® ® /// \$\ uo ﬁx [1/ ‘\$K\uoﬁx ® ( (9 pm) 69 ( ® 969 \x \_ ,/ ® ® ® ® ® ® HS Zero lis mega-Cue l l (19 pts) 12. The following is the equation of the electric ﬁeld intensity of an TEM wave. E: 35e-52 sin(47tX106t — 21tz)ﬁx \$51 Be sure to include units in the following (3 pts) What is attenuation constant of the wave? 4 6(ng (4 pts) What is the skin depth? g;_.L-:O.1M (4 pts) What is the wave number? Qzaﬂ/ﬁ‘ (4 pts) What is the wavelength? \$3?an :3? IV l’" / (4 pts) What is the velocity of the wave? .67“! — 5-)” gym/O 3 ~ cAX/oétc'a‘ We” 5 m A- e Cc-o'lX/O f?“ a; 12 (9 pts) 13. Shown are the amplitudes versus position for three TEM waves. What are the standing wave ratios for each? 13 (15 pts) 14. A TEM uniform plane wave is propagating in the +z—direction. The amplitude of the electric A m field is E=10ay % , the wave velocity is 3X108 ? m=3J§x101° s-1 . , and the radian frequency is (5 pts) a)Write the equation describing the electric field. (Not the phasor representation but the actual representation of the electric field.) ‘0 ‘ "9 W 3WXMS=WNO m (10 pts) b) Write the equation describing the electric field if the amplitude of the electric field is still A V l A 1 A E=lan — , but the direction of propagation is in the direction ——ax + —a2 . m «[2— x/E ’\ _> A /\ a A _ 2 __l____ ___l____’\ ﬁvkxaxt a”7’§%‘(wx’0)6/T (W? ‘19 A /\ : [00 ax‘l'lOOdy .5 to ya L (56x, {excl = to co<z(%Uf’></o f 4001 —- Moe a? m ...
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