p240f07mid1_solution - Physics 240 Fall 2007 Exam#1 Please...

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Unformatted text preview: Physics 240 Fall 2007: Exam #1 Please print your name: 0k. v Q (A) [4 Instructions 1. Fill in your name above 2. This will be a 1.5 hour, closed book exam. The exam includes 20 questions. 3,, You may use a calculator, please do not share calculators 4. You may use one 3”x5” note cards with notes and equations you think may be useful. You can write on both sides of the card if you like. Table of constants: y 80 = 8.85 x 10'12 (32/an2 k : 1/(471380) claims—1.6 x 10‘” c qpmton=1.6 x 10'19 C melectron:9-1; X 10-31 kg mpmton=1.617<x10'27 kg Mo = 47: x10"7 Tm/A G = 6.67 x 10'“ NmZ/kgz Version 1 Page 1 1. Four point charges are placed at the corners of a square as shown in the figure. Each side of the square has length 2.0 m. Determine the magnitude of the electric field at the point P, the center of the square. +1140 Th1; ““(qc ccuca{ LEI = K “(“9 + k (“WC/3 r‘ r’” Mp6 __ K 0' A) 3.0x10‘6N/C ’ p ‘WC 4.2 1. FsfiO M/ 1.8x104N/C C C) 2.7 x104N/C D)‘ 9.0 x103N/C E) 2.0x 10‘6N/C 2. Two conducting spheres are far apart. The smaller sphere carries a total charge of . .6 _>< 1‘0”§_\C.» The larger sphere has a radius that is twiCe that of the smaller and is neutral. After thetwo spheres are connected by a long conducting wire, the charge on the larger spheréis' A 2>< 1078 C ‘ ' K I '412‘ 1.0430 Sm: Vj/Q C) 6 >< 10“8 C D) 0 » E) 3 x 10-8 C 3 cc M Q P ’6. . ° G V! Z: (a) -- c? \q I 0 C 'a .— é i i S + 1 I K Q! r 9. r 3 ,3 a ‘1 i s r y a I' a Q 5‘ ’O O -2» 9. g = '7’ )< t 0 Version 1 Page 2 =3; .—=~ smq ”m m 1; (3-60ch '("orcq’ wheik (ides/'38 qcceze/ef'én. (”qr'li‘ [Q we.“ “07L MQCQC> arr/:1 A positively charged particle is placed at rest on one of the electric 1eld lines in the 0 fl . é ‘ S above diagram and then released. Which of the following statements most accurately d ribes its motion? In? Q! 2L4, Its acceleration will always be tangent to a field line. at B) It will move perpendicular to the field lines at a constant velocity. C) It will accelerate perpendicular to the field lines. D) It will move along the field line at a non-constant velocity. E) It will move at a constant velocity along the field line. Use the follovving to answer question 4: The sketch shows cross sections of equipotential surfaces between two charged conductors shown in solid black. Points on the equipotential surfaces near the conductors are labeled A, B, Version 1 Page 3 4. How much work is required to move a +6 uC point charge from B to F to D to A? A) +3.6 x 10"3 J g; zirgjoulgij VCM ~V (B) c 31 o O V‘s/£5. 4-.» f (ml-«(537 _ . X +1.2 10—31 .— ‘3- V6.60 @—3.6:10"3J VJ“ ~ (Mt): Jr a R k? <32” o-Nelz. ijou : 1 AV a, ”3" 5. In Frame 1, two identical conducting spheres, A and B, carry equal amounts of excess A PE charge that have the same sign. The spheres are separated by a distance d; and sphere A exerts an electrostatic force on sphere B that has a magnitude F. A third sphere, C, which is handled only by an insulating rod, is introduced in Frame 2. Sphere C is identical to A and B except that it is initially uncharged. Sphere C is touched first to sphere A, in Frame 2, and then to sphere B, in Frame 3, and is finally removed in Frame Determine the magnitude of the electrostatic force that sphere A exerts on sphere B in Frame 4. 1 A F/3 P. '1 5.7:; é3F/8 ' at C) zero 2‘ D) 3F/4 " _ k (,L 3 (2 E) F/2 2; ~ °- ‘1) 2 :1 F. Version 1 Page 4 6. Which of the following is the best estimate of the capacitance of the Van DeGraaff generator used during lecture? A) 10'4 Farads CqPRC'% C0 O'O‘ SWW B) 10'1 Farads C) 10'7 Farads 10‘11 F arads 10’15 Farads 54".” l0¢ Neu- (D- l“ 7. Charge Q and —Q are connected by a plastic rod of length "d" to form an electric dipole. If a positive charge is placed at point P, then what is the direction of the net force on the dipole? ‘51 E F. _ \ P F + F+ A) T E" D U @¢ C) —> D) (— E) the net force is zero 8. The diagram shows six 6—,uF capacitors. The capacitance between points a and b is: A 3,11F Q 4m: 6yF D) 9yF E) lpF Version 1 Page 5 . 9. Charge "q" is placed on the outer surface of a conducting spherical shell. The shell has inner radius "a" and outer radius "b". What is the electric potential of the inner surface of the conducting shell, relative to zero an infinite distance away from the shell? A) kg 3 ,4+ {MAI outer 1 501+”) 3' Surface = k:— B) kq/a , [a ' C) 0 Pay/0"“ Wart 19 D) k l/a — 1/b) '~ “A “we euQrg ext/Agra, so V s [4’ 1 . A; o (l e M Mr 9 Le r74; 10. 10 C of charge are placed on a spherical conducting shell. A ~3-C point charge is placed C< at the center of the cavity. The net charge in coulombs on the outer surface of the shell '65 O is: > A) —7 B) —3 C) 0 D +3 +7 + at 11. In separate experiments, four different particles each start from far away with the same . speed and impinge directly on a gold nucleus. The masses and charges of the particles are ‘ IL __ K 51 o 3 A U particle 1: mass m0, charge qo "" W‘ V T W particle 2: mass 2mg, charge 2610 ‘2 PM :4 particle 3: mass 21110, charge q0/2 particle 4: mass m0/2, charge 2qo Rank the particles according to the distance of closest approach to the gold nucleus, from smallest to largest. S A) 1and2tie,then3,4 $0... were MOLS‘ B>1>29334 means weré KE ‘Vwa C 4,3,2,l 0,1and2tiefihen4 C(OSZJ” qfafr‘ocl‘. 4, land 2tie, thenl T More circa?) «4W5 {3,00 mane ech'F/OHLQ'F/c. ”PC‘C—Q q/xoo gwr’fiLh-Qf qfq’O/‘OQOL . 2-3 (( QAJA3/ (7b Version 1 Page 6 12. Positive charge Q is uniformly distributed on a semicircular rod of radius "a". If a positive point charge of magnitude Q is placed at point P then what is the magnitude of the electric force that the point charge exerts on the semicircle. T71 ® b, \a 17.3 = O a. S A) F Q2 if — 4'7ngan /\ 7" g q B) F: Q2 / 'H‘CK J 2 Q» Q?“ em = (7%) £352 F = erzgoa2 QF'C (any ill D) J5 2 F = Q 2 f ,L 3.953.. C C9 3 CD 2717900 0‘ Fy‘ * Li’fl" 50 Q Q E) F: Q2 '3. E1: ”280a F :; CQ '9‘ C o 3 (D J (2 X 1 l L! rr to q :5 Use the following to answer question 13: 0. a. The figure depicts the cross section of an infinitely long wire surrounded by an infinitely long concentric cylindrical shell. Each arrow represents exactly the same amount of electric flux. TM {hm amnesia/x coup“: (was. 3;»: grams 002+; anfiq 3'“ 7 I’ll -.—_~ {Fwy Q‘FOWS W 0ch Stu-Qch Vie/{Stnslfagja qnows fec'nllll’tjfih‘r? ‘ IQ ‘1(F°"V: 2 cal-Who)? . 13. If the charge per unit length on the wire is A then what is the charge per unit length on the cylindrical shell? A))\ Bi 0 .. l? ArrowS .—.— QOM‘I D) -)\ ~3 C6 Arrows 3 7— fivul’ I E)-2)\ “3 _$lfi=90a+Q §q0u1;*33 Two infinite slabs are placed parallel to each other. The slab on the left is an insulator and has a surface charge density of , (I placed on its right side. The slab on the right is a conductor with a net charge of zero. What is the surface charge density on the left side of the conducting slab? l4. mrface Cat/Lag“ Q+OF ‘ (.5 A2 :4 7‘7“”! / charm: g S'o e‘lL WUS7L hat/L ’0, G"; ¢?U¢i/ OtMou/UQLS . o~l> 0/349‘ Chewy/Q 0A Insulator Sign“ L e“ C” L I {6&2 9° —/2 C) ;: (cmucfiK Beta "0"; D E)) 3/2 00w? 0* froaQ/uae 140.0% 7‘49"! W (90”!{3 (Lab-é 0" frodoaoas Nol‘, kt’l‘w’uw S‘Qtég‘ 441M “that POUN/S ”34+ +Luz O-Z‘g Loucoz( 2:: 4' 7;, O: OLfkcg a” 9,664 .5 24. Te: _, g o (E _! U. 0146 ‘ "2., OZ 1 :1: A 15. Three charges are connected by insulating rigid rods of length "d" as shown in the diagram. If the rods are removed and the charges are allowed to separate then what is the total kinetic energy of the system after they have moved a very long distance apart? W/W/WM t L '3 0&4 /> FE ? O Q Q Q WC) ‘lQEg '3 PE: PF. r.— E42139; *0 WM ’1 Fla-we 1 “ 13.95:" 1 P I = I; z 1‘ S2 A) (5/6) sz/d “ ‘2. ., ‘9‘ A p“ T .(5/2)kQ2/d {9}ch 3 .- afE‘ —_— kQ- 40" C) We need to know the masses of the charges to find kinetic energy. 7 4' -—-. D) (1g) kQZ/d «of E) kQ/d fo’er‘k APE r: EEC-‘4‘ «L 7 16- The electric potential in a region of space is V = C ln(x2 + y2). What is the electric field on the x-axis? A) 0 A B) 2Cx A 2Cy A .. x2+y2x+x2+y2y E w v V C) 2C2 A x2 + y2 Z E $ :2, _, C) V D) 22ch 3c 9 x x + y 2C , A , x x ~ & L X :5 1C; )9 "‘~ '< ‘0 3-“ j 1.. a X is :2 fl Q C 93 i “1‘“ -—; O X 1‘ \j " (j a C) Version 1 Page 9 . 17. Two uncharged metal spheres, L and M, are in contact. A negatively charged rod is brought close to L, but not touching it, as shown. The two spheres are slightly separated and the rod is then withdrawn. As a result: Na?) a foul (“6% L M Jr‘II,‘II'F pohuflas twuo " SfW 5. WW ("W ‘3 M Sef‘iquo/ Ottawa}? 0‘5 (Star/76% insulati ng sup parts A) both spheres are neutral B) both spheres are positive C) both spheres are negative D) L is negative and M is positive @L is positive and M is negative 18. Point charges are located at two vertices of an equilateral triangle and the electric field is zero at the third vertex. We conclude: .——>- . ( A) the two charges have opposite signs and the same magnitude E ¢°L ‘4 O 4 "j . B) the two charges have opposite signs and different magnitudes 6‘1 2‘ 00 O: l 0V! C) the two charges are identical D) the two charges have the same sign but different magnitudes i Luz 3 “M lflufi “row A fig 19. Charge Q is on the y axis a distance a from the origin and charge q is on the x axis a C. (L fir distance d from the origin. The value of d for which the x component of the force on q is $5”, the greatest is: A) O B)a J > Zen/em q MM Q.fi gosmc= ¢ w~ e: D) my J} fires-«4+. @am at least one other charge is present fioes -~ 092.. E c W = Q . Elf...“ mg gravid“ (2X Joe C(G’Mhadg)?1 C(31_\,di.)-i Version 1 Page 10 $ 2. 2 ~__t C2360 ' l— 330 a CD 54:91”! . 20. A uniformly charged thin ring has radius 15.0 cm and has total charge +6.0 nC. An electron is placed on the ring’s axis a distance 30.0 cm from the center of the ring and is constrained to stay on the axis of the ring. The electron is then released form rest. Find the speed of the electron when it reaches the center of the ring. A) 1.00 x105 m/s B) 3.0x108m/s , _. IcQ C) 1.5x107m/s V; " N c L3 D) Om/s I" gig—22 @83x106m/s V r k Q G <1 AU 2 5;" kQ .. \fl Q Wag Ls E t ‘° 2% Av V0 . “C a a“ *"APE: Version 1 Page 11 ...
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