Name: Toal Poins: (Las) (Firs) Muliple choice quesions [1 poins] Answer all of he following quesions. Read each quesion carefully. Fill he correc bubble on your scanron shee. Each correc answer is worh 4 poins. Each quesion has exacly one correc answer. Quesions 1 hrough 6 all refer o he same problem. Consider he circui below, consising of a baery, swich, wire, and wo oher circui elemens, denoed by boxes 1 and. The graphs below represen possible measuremens of he poenial difference, V =V a -V b, across circui elemen versus ime. Time = (verical line) denoes he ime he swich is moved. The horizonal line denoes V =. For each of he following cases, choose he appropriae graph for he poenial difference measuremen across elemen. S1 S 1 a b V A B C D E
Name: Toal Poins: (Las) (Firs) Quesions 1-3: The swich has been in posiion S for a long ime. A ime =, he swich is moved o posiion S1. 1 Box 1 = resisor, Box = capacior A. graph A B. graph B charge of he capacior VC = Vba ( 1 e ) C. graph C D. graph D E. graph E Box 1 = inducor, Box = resisor A. graph A B. graph B VR = IR = Vba ( 1 e ) C. graph C D. graph D E. graph E 3 Box 1 = capacior, Box = resisor A. graph AVR = IR = Vbae. For <, V R = since here is no curren. B. graph B C. graph C D. graph D E. graph E Quesions 4-6: The swich has been in posiion S1 for a long ime. A ime =, he swich is moved o posiion S. 4 Box 1 = resisor, Box = capacior A. graph A B. graph B C. graph C D. graph D E. graph E discharge of he capacior V = V e. For <, V C =V ba 5 Box 1 = inducor, Box = resisor A. graph A B. graph B C. graph C D. graph D E. graph E The inducor opposes he change of he curren. I keeps he curren running for a lile while: V R C ba ba = IR = V e. For <, V R =V ba
Name: Toal Poins: (Las) (Firs) 6 Box 1 = capacior, Box = resisor A. graph A B. graph B C. graph C D. graph D The curren flows in he opposie direcion (he capacior is being discharged). VR = IR = V bae. For <, he capacior is fully charged and here is no curren. E. graph E Quesions 7 hrough 9 all refer o he same problem. Consider he circui below. I conains a baery wih emf V b = 1. V, a swich S, a resisor wih R = 1 Ω, and an inducor L wih negligible resisance. A volmeer is in parallel wih he inducor (assume ha he volmeer has an infinie inernal resisance). The swich is closed a ime = s. 3 A ime = 5. 1 s afer he swich is closed, he volmeer reads V=3.68 V. S V b =1V R=1Ω L V 3 7 Wha will he volmeer read a ime 1 = 1. 1 s? A. 7.36 V B. 1.35 V V = V e b Thus, V ( ) = V e C. 1.84 V D. 6.1 V E. 6.3 V 1 b 1 = V e b = V b V ( Vb ) 3.68 = 1 1 8 Wha are he unis for he value of he inducance A. esla B. weber C. henry D. ohms E. farad 3
Name: Toal Poins: (Las) (Firs) 9 Wha is he magniude of he value of he inducance (in he above unis)? A..5 Use V = V b e and B. 5. 1 C. 5. 1 D.. 1 E. 5 5 4 = L R, hus L = R V ( ln V b ) 4
Name: Toal Poins: (Las) (Firs) Quesions 1 hrough 19 all refer o he same problem. The picure below shows wo curren-carrying wires. A long wire parallel o he y-axis crosses he x-axis a x = 1. cm and carries an upward curren I 1 =. A. A square loop of side a = 1. cm lies in he xy-plane, cenered a he origin. I carries a counerclockwise curren I = 3. A. The +z direcion poins ou of he page. y 1 cm I 1 =. A I = 3. A 1 cm x 1 cm Quesions 1-1: Wha is he magneic field vecor (direcion, unis and magniude) along he righ segmen of he loop (a x = 5. cm) due o he verical wire? 1 direcion? A. +x r r µ Idl rˆ C. +z Use he righ hand rule and db = 4π r D. -x E. -z dl r is along +y, rˆ along -x 11 unis? A. ampere B. weber C. vol D. farad E. esla 1 magniude (in he above unis)? 5
Name: Toal Poins: (Las) (Firs) A. B. C. D. E. 6 Apply Ampere's law: Take as a closed pah a circle in he xz plane 8. 1 of radius 5cm and cenered a x=1cm, z= cm. π rb = µ I1 Thus 7 4π 1 B = π.5 5.5 1 5 1. 1 6 4. 1 8 8. 1 Quesions 13-15:Wha is he force (direcion, unis and magniude) on he righ segmen of he loop (he porion wih x = 5. cm, 5. cm < y < 5. cm) due o is ineracion wih he verical wire? 13 direcion? 14 unis? r r r A. +x F = I l B and I l r is along +y, B r along +z C. +z D. -x E. -z A. newon B. newon/meer C. esla D. vol.meer E. vol/meer 15 magniude (in he above unis)? A. B. C. D. E. 1.6 1.4 1 3.6 1 6. 1 1. 1 6 6 6 6 5 r F r r = I l B, F = 3.1 8 1 6 16 The direcion of he ne force on he enire square loop is A. +x From 13, he force on he wire a x=5cm is along +x. The force on he wire a x=-5cm is along x and is less han he force on he wire a x=+5cm, 6
Name: Toal Poins: (Las) (Firs) since he wire is farher away. The forces on he wires a y=+5cm and y=- 5cm cancel ou. C. +z D. x E. no direcion (F=) 17 The direcion of he ne orque on he enire square loop is A. +z C. z D. y E. no direcion (=) All of he forces acing on he loop go hrough he cener of he loop. Quesions 18-19: The square loop is now roaed so ha i lies in he yz-plane, cenered a he origin. I carries a counerclockwise curren I = 3. A as viewed from he verical wire. The wo verical segmens (a z = ± 5. cm) are equidisan from he verical wire (which is sill a x = 1. cm, z = ). y I 1 =. A 1 cm 1 cm I = 3. A x z 1 cm 18 The direcion of he ne force on he enire square loop is A. +x C. +z No force on he wires a y=+5cm and 5cm. For he wires a z=+5cm and 5cm, see drawing on he righ. F B z B F Top view: y ou of he page 7 x
Name: Toal Poins: (Las) (Firs) D. x E. no direcion (F=) 19 The direcion of he ne orque on he enire square loop is A. +z C. z D. y (see drawing above) E. no direcion (=) 8
Name: Toal Poins: (Las) (Firs) Quesions hrough 3 all refer o he same problem. Consider a square wire loop of side a lying in he xy plane, cenered on he origin, as shown below. The +z direcion poins ou of he page in his drawing. y B r a a x Quesions -5: A uniform magneic field r B = Bzˆ fills he region (field lines direced ou of he page). The magniude of B r is B=B. Wha is he magniude of he ne flux hrough he loop? A. B Φ=B a aking he area vecor along +z a B. 4aB C. B a D. E. π B a π Ba 4 Quesions -5:The magneic field magniude is decreased linearly from B o in a ime, i.e. B = B 1 Quesions 1-: A ime =, wha is he induced emf (unis and magniude) around he loop? 1 unis? A. newon B. joule C. esla D. vol E. ampere 9
Name: Toal Poins: (Las) (Firs) magniude? A. B a Ba B. dφ d db d Φ = Ba, emf = = a = (independen of ) Ba C. πba D. E. No enough informaion 3 The direcion of he curren in he op segmen of he loop (a y = +a /) a ime B a = is A. +x (clockwise in he loop) B. x (counerclockwise in he loop) To compue he flux, we chose he area vecor along +z (ou of he page). The posiive direcion around he loop is counerclockwise. Since he emf is posiive, he curren flows in a counerclockwise direcion. C. no curren in he loop 4 The direcion of he ne force on he square loop a ime A. +x C. +z D. -x E. No direcion (F=) (see drawing) = B r is F F I F 5 The direcion of he ne orque on he square loop a ime = is F A. +x C. +z D. y E. No direcion (=) All of he forces go hrough he cener of he loop 1
Name: Toal Poins: (Las) (Firs) Quesions 6-3: The magneic field is reurned o is original value (B=B ). In a ime 1, he angle θ beween he loop and he xy plane is increased from o 6, i.e. o θ ( ) = 6, and hen held a θ = 6. In he op view of he square loop below, +y 1 poins ou of he page. x θ r B = B zˆ n z 6 A ime = 1 (θ = 3 ), he magniude of he flux hrough he loop is A. increasing B. decreasing Φ=B a cosθ and cosθ decreases as θ goes from o 6. (ake he area vecor, n, as indicaed on he figure) C. no changing 7 The direcion of he curren in he op segmen of he loop ( a y = +a /) a ime 1 = (θ = 3 ) is (referring o he figure above) A. owards he op righ corner of he page dφ B. owards he boom lef corner of he page emf = >. The posiive d direcion around he loop is se by he choice of he area vecor defined in 6. C. no curren in he loop 8 The direcion of he ne force on he square loop a ime A. +x C. +z = 1 (θ = 3 ) is 11
Name: Toal Poins: (Las) (Firs) D. x E. no direcion (F=) Since B is uniform, he forces on any wo opposie sides of he square loop cancel ou (same B, same lengh, opposie direcions for he curren). 9 The direcion of he ne orque on he square loop a ime A. +x = µ B, µ is along n, B is along z C. +z D. y E. no direcion (=) 3 The magniude of he induced emf in he loop is larges a = 1 (θ = 3 ) is Α. θ= Β. θ=3 C. θ=45 dθ π D. θ=6 emf = Ba sin θ = Ba sin θ.for θ beween and 6, sinθ is d 3 larges a θ=6. E. all angles beween and 6 (he emf is consan) 1 1
Name: Toal Poins: (Las) (Firs) PROBLEM 1[4 poins] Equipoenials in a plane perpendicular o 3 charged rods are shown in he figure below. The rod on he lef has charge +q. The wo rods on he righ have charge q. The line connecing poins BCD is a field line. The poenial difference beween adjacen equipoenials is 1. V; he V= equipoenial is labeled. -q +q -q 1). [1ps] On he figure, skech he elecric field line ha passes hrough poin A (marked wih black do). Use an arrowhead o indicae direcion. The elecric field line is perpendicular o he equipoenial lines. The elecric field is direced from +q o q. ). [1ps] Find he elecric poenial a poins A, B, C and D. Explain. Coun he number of equipoenial lines from he poin o he V= equipoenial line. Use ha V=1V beween wo adjacen field lines. V decreases in he direcion of he elecric field (which is from +q o q) V A =+1V, V B =+5V, V C =+1V, V D =-1V 13
Name: Toal Poins: (Las) (Firs) 3). [1ps] Rank he magniude of he elecric field a poins A, B, and C. Explain. The smaller he spacing beween he equipoenial lines, he greaer he elecric field V since E = r The spacing beween he equipoenial lines is smalles a B, hen a C hen a A E A <E C <E B 4). [1ps] How much work is done by he elecric field in moving an elecron from poin A o poin D? Jusify your answer. Is he work by he elecric field posiive or negaive? Explain. D W = q( VA VD ) = e(1 ( 1)) = ev = 3. 1 The work done by he E field on he elecron is negaive. A 19 J 14
Name: Toal Poins: (Las) (Firs) PROBLEM [4 poins] In he circuis below, bulbs 1-5 are idenical, and he baeries are idenical and ideal. Boxes X, Y, and Z conain unknown arrangemens of bulbs. I is known ha R x =R y >R z 1 4 + _ X + _ Y 3 + _ Z 5 1). [1 ps] Rank he poenial difference across box X, box Y, and box Z in order of increasing absolue value. Explain your reasoning. Using Kirchhoff s rule for he 3 circuis: V ba =V X +V 1 V ba =V Y +V V ba =V Z +V 4 The oal resisance of he circui conaining X is greaer han he oal resisance of he circui conaining Y. This is because here is an exra pah provided by bulb 3 in he circui conaining Y and ha R X =R Y. Thus he curren hrough bulb 1 (=curren hrough he baery in he circui conaining X) is greaer han he curren hrough bulb (=curren hrough he baery in he circui conaining Y). I follows ha V >V 1. Then using he firs wo equaions above we find: V X >V Y The oal resisance of he circui conaining Z is less han he oal resisance of he circui conaining Y since R Z <R Y. The curren hrough bulb 4 is greaer han he curren hrough bulb. I follows ha V 4 >V. Then using o he las wo equaions above, we find V Z <V Y. To conclude: V Z <V Y <V X ). [1 ps] Is he brighness of bulb 3 greaer han, less han, or equal o he brighness of bulb 5? Explain. We have V 3 =V Y and V 5 =V Z, hus V 3 >V 5 The greaer he volage across a ligh bulb, he brigher he ligh bulb. 3 is brigher han 5. 15
Name: Toal Poins: (Las) (Firs) 3). Rank he brighness of bulbs 1, and 4 in order of increasing brighness. Explain. From he above discussion, V 4 <V <V 1 The greaer he volage across a ligh bulb, he brigher he ligh bulb. Thus in order of increasing brighness: 1<<4 4). [1ps] Suppose a second box idenical o box Z is conneced o he circui as shown. Deermine wheher he brighness of each of he bulbs below will increase, decrease, or remain he same. Explain. + _ 4 Z 5 Z a. Bulb 4 Since he oal resisance of he circui decreases (one exra pah), he curren hrough he baery increases. The curren hrough 4 is he same as he curren hrough he baery. 4 ges brigher. b. Bulb 5 V 4 +V 5 =V ba V 4 increases since 4 ges brigher. Thus V 5 decreases, and 5 ges dimmer. 16