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FinalFall2008Solutions

# FinalFall2008Solutions - Section(check one Jiao Meiloch EE...

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Unformatted text preview: Section: (check one) Jiao Meiloch EE 311 Final Exam Fall 2008 December 19, 2008 Closed Text and Notes 1) Be sure you have 18 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 (5 pts) 1. In spherical coordinates, a unit normal vector to the plane (15 = 45“ is A) ar B) a” We D) none of the above (6 pts) 2. Convert the point (2, 45°, 45°) in spherical coordinates to rectangular coordinates. 2: if“ (“Er-“Q :7 WWW WW“. I: i i}; :: l" i“:- Q; J” "'2 (6 pts) 3. The intersection of the surfaces defined by p = 10 and cf) = 31/4 is a a) a point straight line c) a circle (1) a plane 6) a cone d) a cylinder (6 pts) 4. In free space a plane of charge 17.708x10'l2 CM2 is located at z 2 —1 m. The electric field intensity at the origin is, a) gamma-Hazy"— m b) —8.854x10"2€z31 m "7% c) 331:1 m d) Jazz m e) none of the above 4 (8 pts) 5. The sliding rod in the following figure is being pulled in the +x direction as shown at 1 m/s on two rails that are separated by 1m. Everywhere is a magnetic flux density of lOEzzT e} (5 pts) What is the current ﬂowing through the resistor? (A t: W (MA A m ' ' 97/? 2.7355) (law) (i m (A :~: (to (i m) (3*) "If: Iva“ :1 (i a} (ix‘i , .. A J > tea-"é, “zit-r ‘ "“ M l (3 pts) With an arrow on the figure indicate the direction the current is flowing. 5 (12 pts) 6. For the currents and closed paths shown, calculate the value of the indicated integrals. L2 L1 20 A 10A ® L3 L4 20 A 09 10A gSH-dl: gSH-au: w- ¢H.dl= (:2 [q gnu-ax: géﬁffi (6 pts) 7. Suppose a uniform electric field exists in the room in which you are taking this exam such that the electric field lines are horizontal and at right angles to one wall. As you walk toward the wall from which the electric field lines emerge into the room, (so if you were a positive charge you would be pushing against the force due to the electric field) are you walking toward a) points of the same potential (along an equipotential line). b) points of lower potential. @points of higher potential. (6 pts) 8. A parallehplate capacitor connected to a battery stores twice as much charge with a given dielectric as it does with air as dielectric. The susceptibility of the dielectric is @1 C‘Wé‘f‘é"; at (2" ’Lgn’ 026‘), 2V C)2 I h ‘5 [ﬁt (I :3? 02 Cl D)3 é um {i} ' ﬂ m Q. T: 3 43“ j: “ {glam-C 02 6:361 W/ £95“ a); E)4 3" 0613i (26”? H / 6 (10 pts) 9. The region for z < 0 is free space and for z > 0 a dielectric of relative dielectric constant 2. There is a sheet of charge on the xy plane of 1%. If the electric field for z < 0 is, m 2 I 7 a. K— , then the electric field for z > 0 is, =Wa. + ———-—-———a — 8.854x10"l2 * sssmo“2 ’+ 8.854x10“12 ‘m . rs {gm rm f y: k — 2 I 4 K ‘ ‘ : .. (.3913 " 8.854x10‘” a‘ + 8.854x10"'2 at + 8.854x10‘” 3“ m Calf) m m {4’ 6} M26 Dash? (SW A"??? E 2 1 5 V b)Em——~—-—lzax+—_na +mn—MWW—12az— » 8.854x10‘ 8.854x10 3“ 8.854x10" m (M (3, \$4 W, W C) E=Mmmgfmﬁax +____._L__.3a +¥ﬂayl€ 2"“ 8.854x10" 8.854x10 y 8.854x10 ‘m ém f, «~14 I 3 2 5 V d E: ——a. + WWW—a +——-—~——a. — M -......,.....M....,.. ) 8.854x10‘” " 8.854x10““2 3’ 8.854x10‘” ‘ m e “We” f elm—1...... .La .Waz M4; fie 8.854x10‘” ‘ 8.854x10‘12 3' 8.854x10"'?’ z m T M L . 13% {-3) ('7‘) g; s f) none of the above p ~ ’V‘ 3' “’3 2 ” .‘ m ._ a .. r . (10 pts) 10. Flowing in the x lane is a sheet cuififent density of ~65: . Derive the ma neg? fieid intensity 3’ P .i m g everywhere. (Hint use Ampere’s circuit law.) .ﬂ- h r ‘ Kil- H W“ 7 jg: ﬂ h \$1.... “at; 1::2'w' “7" . ---' ww—me: r< " an “" «’1' ‘f: 12%“ H: “57’ I A; W mi" W £31} )1 w-- «e~ :m3w«+ gig 02 H- : ~ m ‘7 #:3ﬁ m I‘m 7 (10 pts) 11. How much energy is stored in a collection of three +1C charges that are all in a line and with l m between them as shown? . 1 m 1 m H“ ‘ W. ﬂ f M M (cw 6C '3 Z 6r}; (’3 V; j? go (rm) mi Wig, LIME d "I; (.1, 1: 8r) 61¢, tr :2 “‘ M mi? g; 2. 2 1 to (1 ﬁg is: airwﬁﬁﬁaaw W 2“ 02 ngt ,1“: wr- :1 aJHJgX/C} ]“ r: I c; (10 pts) 12. The region for z < 0 is free space and for z > 0 a non—magnetic material with relative dielectric constant 2. There is a sheet current density of 4521i flowing on the xy plane. If the m magnetic field intensity for z < 0 is, H n ZaK + laJr + 421z £, the magnetic field intensity for z > 0 is, m a) H=2ax -+- lay +4az£ m A d) H=2ax +033, +2az—m m A b) PI=2aV + lay +531;— . m A e) H2 lax +121y +5az— m A c) HaZax+lay+3az4 m (6)10ne of the above 8 (15 pts) 13. The region of space for z < 0 is filled with a dielectric of dielectric constant e, = 2:3” and permeability M0. The region for z > 0 is filled with a dielectric of dielectric constant 52 and permeability it”. The electric fieid for z < 0 is given by E(x,r) : 300031(2.51x10‘5)tw (1.26 ><107)z]aK —lOcos|(2.51x10i5)t+ (1.26 x 107mg.x K m (5 pts) What is the Standing wave ratio? gmt 57? a) L4 (5 pts) What is the reflection coefficient? (5 pts) Give an expression for the magnetic field for z < 0. H (1} ﬂ ‘3: 5' agggiwesﬂ {ﬁMX/éi) "fl ‘7} 9 (20 pts) 14. Answer the following question for an electromagnetic field that has the following magnetic field intensity that is described by Hm) n 3OCOS[(1.26X1015)t+ (1.26 x107)x]\$slz (5 pts) The frequency of the wave is @x1 014 Hz B) 1.26 x iotHz C) 2x106Hz D) 1.26x10‘5Hz (5 pts) The wave number of the wave is A) 1.26x10ms'l @126x107m" C) 1x108 D) none of the above (5 pts) The velocity of the wave is 4 "3’ A) 1x 10836;. (“’1’ s L [,5 :2 B)1><108ﬂ&E S C) IX 1083sz S @ﬁ—lxlosgﬁx D) —3 x 103—9":sz S (5 pts) The wavelength of the wave is A) 4.99 x 10‘35m 3; W @3")4.99 x 10'7m" / C) 1.26 x107m D) 1.26x10'5m 10 (10 pts) 15. Two point chare 0f —2 nC and 1 nC are placed, respectiveiy, at (0, 0, 1m) and (0, 0, 2m) while an infinite conducting plane is at z z 0. (2 pts) How much charge is induced on the piane? 4.. n (8 pts) What is the f0rCe 0n the i nC charge? a» 4» A (12m 6* '“a‘lr‘ C. A Em mm W W " {Aim elm ﬂ ‘Wlm <1 ‘1 '3‘ WM C “(:3 l .cth‘Cyéané/j‘ ((nébézné.\ (in¢\é‘lw() 6/? F “'.‘.1-- WT , + N - 4— h .2. VJ“! 6m Cyan) w, Wig)? ’ Mia? 1 «W t #1700 (:2 QX/o; CL 1X10 (2" A W“: €13 ML me» [We % ~ t MWX/“W cl. A m ,W WW V 6? ~- A . 42; , Wﬁ(§r3’g‘/X/O WE” ’74 Z: {W My A C 2. Cl. C Ix” / A; Mm %M W“! 11 (15 pts) 16. Consider a structure consisting of two plates of width w and separation (1. Assuming w >> (I, determine the inductance per unit length. Hint the condition w >> (1 allows you to determine the magnetic field between the plates as if the plates were infinite in extend. Aiso, if the current in the top piate is I as shown, the current flowing in the bottom plate is "—I. 12 (45 pts) l7. Indicate whether the following statements are true or false. In an orthogonal coordinate system, the coordinates are mutual! ‘ Tru- perpendicular. The magnetic flux density is a scalar r' - Electromagnetic waves travel faster in dielectrics than in free space The frequency of an electromagnetic wave remains the same as it travels r from free space into a dielectric. r False In a linear dielectric the polarization field varies linearly with the electric field intensity. The electric field intensity for an equlpotential object is always tangential to True " False”- the surface. \ ' True' ' False r The displacement current density is the time rate of change of the electric True False flux density. N The magnetic flux density is measured in T or thm2 ( False If the current is doubled flowing through a wire coil, the inductance of the True Faisg coil is doubled. W“ Two waves of equal magnitude, but propagating in opposite directions, will ‘ False result in a standing wave. tolerate or Withstand without electric breakdown. In a lossy dielectric the electromagnetic wave loses power because of reflection of the wave. A polarizatiori fieid cannot result from an applied electric field in a materiai made up of non—polar atoms 01' molecules. In a ferromagnetic material like iron, the individuai atoms have lar permanent magnetic dipole moments. ...
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