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final_exam_from_spring_04_1

# final_exam_from_spring_04_1 - FINAL EXAM GENERAL PHYSICS 11...

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Unformatted text preview: FINAL EXAM GENERAL PHYSICS 11 SPRING QUARTER 200M .June 8, 2004 Student ID # Lecture Instructor Section Number Full credit will only be awarded to answers with all work shown. 1/4mc,0 = 9 x109Nn12/C2 a=835x10”CWan p.o=47tx10'7 Tm/A mp: 1.67 x10'27 kg me=9.11x10'31kg e=1.6x10"9c PROBLEM SCORE 1. / 25 5 / 25 2. / 25 6. / 30 3. / 20 7. / 20 TOTAL SCORE (230/ 200) 4. / 25 8 / 60 PROBLEMS W 1. A solid conducting sphere of radius 3.00 cm has a charge of 12.0 uC. A conducting spherical shell of inner radius 5.00 cm and outer radius 8.00 cm is concentric with this solid conducting sphere and has a total charge of -4.00 uC. The distance of a point from the center of this charge conﬁguration will be denoted by r. Find the magnitude and direction (if any) of the electric ﬁeld at: a) r = 2.00 cm, b) r = 4.00 cm, c) r = 6.00 cm, (1) r = 10.0 cm. e) Determine the total charge residing on the inner surface of the conducting shell. UA—t’ Galaxy: '4, L a r , ’4’ F M ’41 477112 f =‘ Z~ 1» W 60 W ‘ t: a _.: )2? g.» = 45 W a Q) /’:o] WW 0 W15 C?) 00 5"”: [anal/5'2 E’7‘ 7M? gi/zzéﬁ L’ e> FW‘WC‘LEKI/VC ’— mmm. J grill;— 2.A. In ﬁgure below, point P is at the center of the rectangle. With V = 0 at inﬁnity, what is the net electric potential at P due to the six charged particles (in terms of q, d, 85, and 1t)? +5.0q —2.()q ‘ —3.0q Wei—«we»? d 0P d +3.0q —2.0q +5.09 14 i i ‘1' VP: VP: 1 = i=1 1 i=14ﬂ£0ri 1 5. Oq — 2.0g — 3.0q 3. Oq —— 2.0q 5.0q —-— ———————-—+———+~———-————+————-——+————+—-————-—— = 47‘50 w/d2+(d/2)2 W2 WWad/2f w/d2+(d/2)2 61/2 WWWI/2)2 l 10.0q - 4.0g 1 10.0q -— 4.0q 2g ——-———+ = ————+ = 10/6—4 = 47:50 (d2+(d/2)2 d/2 4zao[(d/2)J§ d/2 47rgod( ) 0.94q 4759061 2.B. In ﬁgure below, how much work is required to bring the charge of +5q in from inﬁnity along the dashed line and place it as shown near the two ﬁxed charges +4q and -2q? Take distance d = 1.40 cm and charge q = 1.6 x 10’19 C. +4q +5q @«—————— 2d 43° 50° /’ d // O / / / —2q ,1 ml W=AU= 1[moob+obemq=o 4ﬂ‘80 2d d 3. gar—Mill» For the circuit below, calculate the values of the currents 11, 12, and 13 for the directions indicated on the circuit diagram. éuias‘t‘;‘fa‘7ra7 1 any 216%.; ides r? , if h I 9" Bfﬁ‘rrawzfa :3 ‘i— M; 3. 5 591,7“th 3) 7159 £51- {My 7,411— 513:0 :20 ~ 20 W11}. 7?£a.13. 4; +0 ’ U5 7 ¢ 9 OK “‘5 4. Three very long straight wires are arranged as shown in the diagram below. The +z axis is directed out of the page. Wires 1 and 2 are parallel to the z-axis at (x = -a, y = 0) and (x= +2a, y = 0), respectively, and carry constant currents of 11 and 12 into the page. Wire 3 is parallel to the y-axis at (x = a, z = 0) and carries a constant current of 13, along +y. , (a) Find the magnetic ﬁeld, B, at the origin, in unit vector notation, Bx i + By j + Bz k, in terms of 11, 12,13, a, no and 11:. ' (b) Find the magnetic force, F, that would be exerted on a charge q which is at the origin and moving at a speed of v along the +y direction. Find the force, F in unit vector notation, FX i + Fy j + F2 k, in terms ofIl, 12, 13, a, 110, q, v and 1t. F 3 14,247. 4!: A, I; L. Zen bl/ -/’// ﬁg 8 06c“; ’ 5. A conducting rod of length L = 10. cm is pulled along two horizontal frictionless conducting rails at a constant speed of v = 5.0 m/s, as shown in the diagram below. A uniform magnetic ﬁeld of magnitude B = 1.2 T is directed out of the page. The resistance of the rod is 0.40 '9. The conducting rails are connected by a fixed metal strip at the end opposite the rod, and the resistance of conducting rails and metal strip is negligible. (I 0) (a) What is the induced current in the loop formed by the rod, rails and strip? Indicate on the diagram in which direction the current ﬂows through the rod. (5‘) (b) What force must be applied by an external agent to the rod to keep it moving at its constant velocity? (0) What is the power loss due to joule heating in the rod? ‘6) 6) (d) What is the power provided by the external agent to keep the rod moving at its constant velocity? 9 a C G a a x ‘ I " 7km; N; ew C‘jggkwﬁﬁ 7h jaof‘ ,ois ) - an - ( “ac/.00 i1 3 ('5 I5 éifasﬂo M: 3211' )2; off?” ‘ C c R 3'9} K g , {L2 7'3[0»/?::%>{§I<€T<’§2 .2. LEA . . ‘ "t ' 5:... {a 3 awagseé. -: 45119915.): W )s 554” . ,_.. K I V \\ "\ Q v at) \l . ‘V '2 if ~ (K, We ‘?._.,.<’i?/6A) I’M” .1 ..... ‘J ﬂ if 2 W '0 Wes {arilltmi'iﬁzzzn’mdsw ;A r 20 mi?“ Wig is stretched 9.80 cm when a 300 g mass is suspended from it. The spring is then stretched an additional 10.0 cm and released. (a) What is the frequency of oscillation of the mass? (b) What is the maximum speed of the mass? (K? (c) What is the maximum acceleration of the mass? g I 4' M I" f ‘ ‘ ‘- ‘ '1 \6 (fwd [X .5 :L,5K,2(713m/5>:30/%‘1 Fl: a, 0?? wt Cu 7 : 17’ “4.915 ‘3 Ire — r%§;2;? .— ’-= /0/5 @ w r a @4‘ 3 Wm z 4.0, Is : /g : hf? 252/ I 1. M/s [/‘ccm ) ‘z [00 Gin/9 5 @C H M . '2‘ / a M L “ .31 f; :‘ﬂ‘JI: ’ (6’) av”: AW : {law/’(l’7/5) /‘70 (“/9 > 6B. A 1.0 uF capacitor is connected across a 12 volt battery until it is fully charged. It is then disconnected and connected across a 1.0 mH inductor. a) What is the frequency of the current oscillations in the LC circuit? b) What is the maximum potential energy stored in the capacitor? W (e) What is the maximum current in the LC circuit? I f ‘ ‘ /‘( ‘ ,2} pf? ( 7C '2“ 737 VI; 2W ~77 x} (2'91 Ix! 0 ,/ 7. Two large conducting plates are placed parallel to each other at a distance D apart. The plates are connected byw wires to Box X as shown. When the top plate is lowered, the electric ﬁeld between the plates increases. (At all times the plates are close enough together that fringing effects can be ignored). “9 (a) Is it possible that Box X contains an open circuit, as shown below? Explain No; I; 77a, raw Wefa> (we welded/'11 Boxx Chive 45419557 0% ecu-,L will l‘em’ez‘h [(ﬁhs‘jedi"; 6) “Sh/U“; :2 f 9%,, beﬂnge“ m; Pféas MUSr: ( [(330 fémélw 5641563” U i r (3) K5 lancer/ed, (b) Is it possible that Box X contains a battery, as shown below? Explain . 7’95. if Elia were; (are Cﬁﬂhdo‘féié by 53 Boxx bugslN/l WTetﬁim) cil'f'i’e‘renea.) \/l Y‘Z hath?» (9) emitted, E 7 V/d “7W?” ‘2“ NJ“ \$0 3—? \/ 5 is held ij‘ﬂj Mi d ’5 (Steamser /, E “0:” ibcvaqjﬂ‘ (c) When the topplatejs moved closer to the bottom plate, does the absolute value of the charge density on the top platﬁncmﬂ decrease, or remain the same? Explain , £’ £5) M19891 3Z9 flies) so 9- (b) 6' ‘ "‘ i" w a, 55 Max:252 ﬂit CYZQSOS) l7 rut/‘5} ; (51 f (d) When the top plate is moved closer to the bottom plate, does the capacitance of the pair of platefinm \ / decrease, or remain the same? Explain c, ...__...,r/ (f) a '1 éqﬁ” A re mu}; C “\$767 a“)? M 31 d} clecreacfﬂs a limb C in c Y‘QKS-ZS ,, m” ”' A¢y mmaih zws‘iwil. V can; a” {aways} ’I'Zus C m 1297 {uremia a g‘Yﬁ/ (LQM 8. Circle the best answer for each of the following multiple choice questions. 8.1 A positively charged insulating rod is brought close to an object that is suspended by a string. If the object is re elled away from the rod we can conclude: the object is positively charged B) the object is negatively charged C) the object is an insulator D) the object is a non charged conductor ('13)) _)___ E) none of the above FA ﬂ: = /-’,_’ 3 If r " ( ’3 8.2 Two small charged objects repel each other with a force F when separated by a distance d. If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2 the force becomes: A) F/l6 B) F/8 D) F/2 E) F 8.3 Two spheres, one with radius R and the other with radius 2R, surround an isolated point charge. The ratio of the total -\ mber of electric ﬁeld lines that pass through the larger sphere to the number through the smaller sphere is: B) 2 C) 4 D) 1/2 E) 1/4 8.4 Two point charges, ql and q;, are placed a distance r apart. The electric ﬁeld is zero at a point P between the charges on the line segment connecting them. We conclude that: A) ql and qz must have the same magnitude and sign B) P must be midway between q] and q; GD q] and q2 must have the same sign but may have different magnitudes E) q] and qz must have opposite signs and may have different magnitudes ‘ D) q] and qz must have equal magnitudes and opposite signs )H” = a V x- 8.5 An electron is accelerated from rest throu - . = 2 ~ tial difference V. Its ﬁnal speed is proportional to: A) v B)v2 W D) IN E) V'”2 8.6 Two identical capacitors, each with capacitance 6 uF, are connected in parallel and the combination is connected in d identical capacitor. The equivalent capacitance of this arrangement is: [33_”_. B 6 F C 9 D 12 F E 18 w ) u ) HF ) H ) HF . MP“ 8.7 The re51stance of a rod does NOT depend on: A 1)— » z } A) its temperature B) its material C) its length 6 )1. b ‘7' D) its conductivity ‘5) shape of its (ﬁxed) cross-sectional area a = l;3 -'-""i 8.8 Resistances of 2.0 ’9, 4.0 'Q, and 6.0 'Q and a 24V emf device are all connected in a series irsafi‘rfcuit. The potential difference across the 2.0’ 2. .: ' : I 1' 1742 = 2' Va. =13) '— A)2V w C) 8V D) 12V E) 24V 8.9 A 2 'Q resistor and a 4 'Q resistor are connected in parallel to a 6 V battery. The ate of thermal energy dissipated by theZ'Qresistoris: 7:03: 9 /"-" " 1.”? A) 8 w B) 6 w C) 9 w E) none of these 8.10 At one instant a charged particle is moving in the positive x direction along the x axis in a region where there is a uniform magnetic ﬁeld in the positive 2 direction. When viewed from a point on the positive 2 axis, it subsequent motion is: strai ht ahead around a circle in the x -. around a circle in the yz plane D) in the positive 2 direction E) in the negative 2 direction 8.1 1 A 2.0 H inductor, a 2.0 ’Q resistor, a switch and a 20V ideal battery are wired in series. Immediately after the switch in the circuit is closed the current through the resistor is: A) 6") B)5A C) 10A D)15A E)20A / 8.12 A 2.0 H inductor, a 2.0 'Q resistor, a switch anda 20V ideal battery are wired in series. A very long time after the switch in the circuit is closed the curren - : . ; - \7‘ e resistor is: A)0 B)5A w D)15A E)20A 8.13 A 2.0 F capacitor, a 2.0 'Q resistor, a switch and a 20V ideal batery are wired in series. Immediately after the switch in the circuit is closed the current he esistor is A)0 B)5A C) 10A D)15A E)20A 8.14 A 2.0 F capacitor, a 2.0 ’Q resistor, a switch and a 20V ideal battery are wired in seriesA very long time after the , . ..-..; ' the circuit is closed the current through the resistor is w B)5A C) 10A D)15A E)20A 8.15. A bar magnet is outside of a coil of conducting wire and moving along the axis of the coil, away from the coil, at a constant velocity. The magnetic ﬁeld inside the loop of wire due to the induced current in the loop will be: A zero, since the bar magnetic has zero acceleration 0 in the same direction as the magnetic ﬁeld of the bar magnet inside the loop C) in the opposite direction of the magnetic ﬁeld of the bar magnet inside the loop D) in a direction perpendicular to the magnetic ﬁeld of the bar magnet inside the loop ...
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