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Physics C: Electricity and Magnetism

PHYSICSC Section I, ELECTRICITYANDMAGNETISM Tlme-45 minutes 35 Questions Directions: Eachof the questionsor incompletestatementsbelow is followed by frve suggestedanswersot completions.Selectthe onethat is bestin eachcaseandthen fill in the correspondingoval on the answersheet.

t t

t t

l l

t t

t t

l l

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I

36. Thrce * uF caDacitorsarc connec0ed in seriesas L '

shownin thediagrarnabove.Thecapacitance of thecombination is

.q3

38. A point charge+p is insidean uncharged conductingsphericalshell that in tum is near severalisolatedpoint charges,as shownabove. The electric field at point P insidethe shell dependson the magnitudeoI

(A) ' ' :uF z '

(B) I pF ) (C) +uF J '

(A) (B) (C) @) @)

(D) ' ' +uF z'

I (E) ' - +uF

o '

37. A hairdryeris ratedas1200W, 120V. Its effectiveintemalresistance is (A) 0.1 o (B) l0 o

(c) 12o (D) 120o

(E) 1440O

O only the chargedistributionon the sphereonly Q and the chargedistributionon the sphere all of the point charges all of the point chargesandthe charge distribution on the sphere

39, In a certainregion,the electricfield along the r-axis is given by E=ax+b.wherea=4OYhrP andD=4Vlm. The potentialdiffeiencebetweenthe origin and . r = 0 . 5 mi s (A) -36 V (B) -7 v

(c) -3 v

(D) 10V (E) 16V

734

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charged 42. A2O pF parallel-platecapacitoris fully to 30 V. The energystoredin the capacitoris mostnearlY

Questions40'41 X

X

X

X

(A) 9x103J (B) 9x10-3J (C) 6x 10-4J (D)2x10-4J (E) 2x 10-7J

X

AB

X

X

X

X

X

with A Darticleof charge+e andmass ln moves B field r*"i*r" o"""taictilar to a uniform magnetic a is alr""t"a ioto itt" page.The pathof the particle circle of radius r' asshownabove' the 40. Which of the following correctly gives relating equation the and direction of motion o and r? Equation Direction (A) Clockwise (B) Clockwise (C) Counterclockwise (D) Counterclockwise (E) Couirterclockwise

eBr = mtt eBr = ttw2 eBr = mu eBr = mtt2 eBr2 -- mtt2

41. The period of revolutionof the particle

(A) mr "B (B) 'll^

eE

2nm (c) -E

,-E eB

is

43. '-' A ootentialdifference V is maintainedbetween i*i1**". p*ullel conductingplates'An electron .tu.t. fon te.t on the surfaceof oneplate and acceieratestowardthe other' Its speedas it reachesthe secondplateis propodionalto

(A) ltv (B) ruJV

(c)

(D) v (E) v2

44. A wire of radius R hasa current I uniformly distributedacrossits cross-sectionalarea' l*p"tt;. tu* it usedwith a concenniccircular radiusr, with r < R, to calculatethe oath'of 'maenitude of the magneticfield B at a distance froir the centerof the wite' Which of the following equationsresultsfrom a correct 6r n perc's law to this situation? "ppril"ai" (A) B(2xr) = PoI

@) B(zxr)=

",(*)

Q) BQnr) = o (D) BQrR) = PoI

= @)B(ztuR) ",(#)

(D) '"1

-@(E) .-'"rtl eB

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135


Questions45-46

Q

W

-

4

Q

Particlesof charge Q and-4p arelocatedon the -r-axisasshownin the figure above.Assume the particlesareisolatedftom all othercharges. 45. Which of the following describesthe directionof the electric field at point P ? (A) +r

(B) +v

(c) -v

(D) Componentsin both the -r- and +y-directions (E) Componentsin both the +t- and-y-directions 46. At which of the labeledpoints on the r-axis is the electricfield zero?

47. When the switch ,Sis openin the circuit shown above,the readingon the ammeterA is 2,0 A. When the switch is closed,the readingon the ammeterrs (A) (B) (C) (D) G)

doubled increasedslightly but not doubled the same decreasedslightly but not halved halved

48. Two conductingcylindrical wires aremadeout of the samematerial.Wire X hastwice the length and twice the diameterof wire L What is the p

(A) A (B) B

ratio =l

K..

(c) c

of their resistances?

(A) + (B) +

(D) D (E) E

(c) I (D) 2 (E) 4

136

rlz6d copylng or llut€ ot llrlr Dllc lr lll.od.

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I I I I I

surface'A graphof-electric 49. - A solid metallic sphereof radius ft hascharge Q uiformly distributedon its outer the V as a function of poritioo r is sho'wnabove.Which of the following graphsbestrepresents *tentiaf -magrritude of the electricfield E asa function of position r for this sphere?

(B)

(A)

(D)

I

-----{

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737


50, Two parallel wires, eachcarrying a cunent 1, repeleachother with a force F. If both currents aredoubled,the force of repulsionis (A) 2F

(B) 2JTF (c) 4F @) 4JZF (E) 8r 51. A circular current-carryingloop lies so that the planeof the loop is perpendicularto a constant magneticfield of strengthB. Supposethat the radius R of the loop could be madeto increase with time t so that R = dt, where a is a constant. What is the magnitudeof the emf that would be generatedaroundthe loop asa function of I ? (A) 2nBazt (B't 2nBat (C) 2nBt (D') xBa2t

(E) f;n"2f

'ol-_l-

'^i-l_

€=i

r=

+

lov

'l__l_ , +

f_l-_

20v

I

52. The figuresaboveshowpartsof two circuits, each containinga batteryof emf € and intemal resistancer. The currentin eachbatteryis I A, but the directionof the currentin onebatteryis oppositeto that in the other.If the potential differencesacrossthe batteries'terminalsare 10V and20 V as shown,what arethe valuesof t andr? (A) € =5V,r=15 O ( B ) €= 1 0 V , r = 1 0O ( C ) €= 1 5 V , r = 5 Q (D) € =20v,r=10 Q @) The valuescannotbe computedunlessthe completecircuits are shown. 53. A chargedparticle canmove with constant velocity througha region containingboth an electricfield and a magneticfleld only if the (A) elecaic field is parallel to the magneticfield @) electricfield is perpendicularto the magnetic field (C) electricfreld is parallel to the velocity vector (D) rnagneticfield is parallelto the velocity vector @) magaeticlield is perpendicularto the velocity vector

138

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oirilnr.oop is Pulled

54. A conductingloop of wire that is initially around a magnetis pulled awayfrom tlte magnetto the right, asindicatedin the figure above,inducing a currentin the loop. What is the direction of the force on the magnetandthe direction of the magneticfield at the centerof the loop dueto the inducedcurrent?

Direction of Forceon the Magnet (A) @) (C) (D) (E)

To the right To the right To the left To the left No direction; the force is zero.

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Direction of MagneticField at Centerof Loop due to InducedCunent To the right To the left To the right To the left To the left

55. A squareloop of wire carrying a current 1 is initially in the planeof the pageandis locatedin a uniform magneticfield B that pointstoward the bottom of the page,asshownabove.Which of the following showsthe correctinitial rotationof the loop due to the force exertedon it by the magnetic field? (A)

(B)

(c)


139


I Rz=20 dl

57-5E Quesdons +Q

+9/

.?i

+9...

+a i i+Q

+Q

56. In thecircuitshownabove,theequivalent resistance of thetlu€€resistors is (A) 10.5() (B) 15 ()

(c) 20cr

(D) 50 (, (E) 115O

As shownin the ftgure above,six particles,each with charge+p, areheld fixed andareequally spaced aroundthe circumferenceof a circle ofradius R. 57. What is the magnitudeof the r€sultantelectric field at the centerof tbe circle? (A) 0 9= @) r{o +xeo Rl

Q +raeo + 4Rz (D) iJ2

Q 4xes I8

(E)

3

Q

2xcs L2

5E.With the six particlesheld fixed, how much work would be requiredto bring a seventhparticle of cbnge + Q from very far awayandplaceit at the centerof the circle? (A) 0

(' B ) 6

o

4fteo R

G'+; Q2

R2

,r*

Q,

R

@2-+ E€o 740

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Questions59-61

61. Howmuchnetworkmustbedoneby anextemal forceto movea -1 pC pointchargefromrestat poirt C to restat point E ? (A) -20 uJ (B) -10 rtJ (C) l0 rrJ (D) NN (E) 30 pJ

62. Oneof Maxwell's equationscanbe written as .

The diagramaboveshowsequipotentiallines producedby an unknownchargedistribution. A, B, C, D, and E arepoints in the plane. 59. Which vectorbelow bestdescribesthe direction of the electricfield at point A ? ( ) , / @)

,/

.1A

e. as = -:{3. J0 d t fact that

Thisequationexpresses the

(A) a changingmagneticfield producesan electricfield (B) a changingelectricfield producesa magnetic fie1d (C) the net magneticflux througha closed surfacedependson the currentinside (D) the net electricflux througha closedsurface dependson the chargeinside (E) electricchargeis conserved

(c) \ (D) \ @) Noneof the above;the field is zero. 60. At which point doesthe electric field havethe greatestmagritude? (A) A (B) B

(c) c

(D) D @)E

of tfil.

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qF *d-l 63. The platesof a parallel-platecapacitorof crosssectionalareaA areseparatedby a distanced, as shownabove.Betweenthe platesis a dielectric materialof constantr(. The platesarecomected in serieswith a variableresistanceR and a power supplyof potentialdifference V. The capacitance C of this capacitorwill increaseif which of the following is decreased? (A) A (B) R

65. A physicsproblemstarts: "A solid spherehas chargedistributeduniformly throughout. . ." It may be conectly concludedthat the (A) electric field is zeroeverywhereinside the sohere (B) electric field insidethe sphereis the sameas the electricfield outside (c) electricpotentialon the surfaceof the sphere is not constant (D) electric potentialin the centerof the sphere is zero (E) sphereis not madeof metal

Questions66-67relate to the circuit represented below. The switch S, after being openfor a long time, is thenclosed.

(c) ,
R. It is direcdy proportionalto r when r