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ELECTROMAGNETIC INDUCTION & ALTERNATING CURRENT(QB) WA.pdf
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### MAGNETIC EFFECT OF CURRENT (QB).pdf

1. QUESTION BANK ON MAGNETIC EFFECT OF CURRENT
2. QUESTION FOR SHORT ANSWER Q.1 Consideramagneticfieldline.Isthemagnitudeof B  constantorvariablealongsuchaline?Canyougive an example of each case? Q.2 Acurrentissentthroughaverticalspringfromwhoselowerendaweightishanging.Whatwillhappen? Q.3 B= d 2 / i 0   suggets that astrong magneticfieldis set up at pointsneara long wirecarrying acurrent. Since there is a current i and magnetic field B  , whyis there not a force on the wire in accord with the equation B L i FB      ? Q.4 Two fixed wires cross each other perpendicularlyso that theydo not actually touch but are close to eachother, as shown in figure. Equal currents i exist in eachwireinthedirectionsindicated.Inwhatregion(s)willtherebesomepoints ofzeronetmagneticfield? Q.5 A messy loop of limp wire is placed on a frictionless table and anchored at points a and bas shown in figure. If a current i is now passed throughthe wire, will it tryto form acircular loop orwillit tryto bunchupfurther? Q.6 A verylongconductor has a squarecross section and contains acoaxial cavityalso with a squarecross section.Currentisdistributeduniformlyoverthematerialcrosssectionoftheconductor.Isthemagnetic fieldin thecavityequal tozero? Justifyyou answer. Q.7 Twolongsolenoidsarenestedonthesame axis,asinfigure.Theycarry identicalcurrentsbutinoppositedirections.Ifthereisnomagneticfield insidetheinnersolenoid, whatcanyousayaboutn,thenumberofturns perunitlength,forthetwosolenoids?Whichone,ifeither,hasthelarger value? Q.8 The magnetic field at the center of a circular current loop has the value B = R 2 / i 0  . However, the electric field at the centerof aringof charge is zero. Whythis difference? Q.9 A steadycurrent is set up in a cubical network of resistive wires, as in figure. Usesymmetryargumentstoshow that themagneticfield at the center of the cube is zero Q.10 A copper pipe filled with an electrolyte. When a voltage is applied, the current in the electrolyte is constituted bythe movement of positive and negative ions in opposite directions. Will such a pipe experience a force when placed in a magnetic field perpendicular to the current. Q.11 Magnetic moments arise due to charges. Can a system have magnetic moments even though it has no charge. Q.12 Imagine that theroom in which youare seated is fillled witha uniform magnetic field with B pointing vertically upward.Acircular loop of wire has its plane horizontal . For what direction of current in the loop, as viewed from above, will the loop be in stable eqiulibrium with respect to forces & torques of magnetic origin ?
3. Q.13 Two current-carrying wires may attract each other. In absence of other forces, the wires will move towards each other increasing the kinetic energy. From where does this energy come? Q.14 In order to have a current in a long wire, it should be connected to a battery or some such device. Canwe obtainthemagneticfieldduetoastraight, longwirebyusingAmpere’slawwithoutmentioning this other part of the circuit. Q.15 A uniform magnetic field fills a certian cubical region of space. Can an electron be fired into this cube from the outside in such a way that it will travel in a closed circular path inside the cube? Q.16 InAmpere’s law   B.dl i 0    the current outside the curve is not included on the right hand side. Does it mean that the magnetic field B calculated by usingAmpere’s law, gives the contribution of only the currents crossing the area bounded by the curve ? Q.17 A magnetic field that varies in magnitude form point to point, but has constant direction (East to West) is set up in a chamber . A charged particle enters the chamber and travels undeflected along a straight path with constant speed . What can you sayabout the initial velocityof the particle? Q.18 A charged particle enters an environment of a strong & non-uniform magnetic field varying from point to point both in magnitude and direction and comes out of it following a complicated trajectory. Would its final speed equal the initial speed , if it suffered no collisions with the environment. Q.19 Astraight wire carrying on electric current is placed along the axis of a uniformlycharged ring. Will there be a magnetic force on the wire if the ring starts rotating about the wire ? If yes, in which direction ? Q.20 An electron travelling West to East enters a chamber having a uniform electrostatic field in North to South direction . Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path . Q.21 The magnetic field inside a tightly wound, long solenoid is B = 0 ni. It suggests that the field does not depend on the total length of the solenoid, and hence if we add more loops at the ends of a solenoid the field should not increase. Explain qualitatively why the extra-added loops do not have a considerable effect on the field inside the solenoid. Q.22 Alightening conductoris connected to theearth bya circular copper pipe.After lightningstrikes, it is discovered that the pipe has turnedinto a circular rod. Explain the cause ofthis phenomenon. Q.23 We know that the work required to turn a current loop end for end in an external magnetic field is 2B. Does this hold no matter what the original orientaion of the loop was ?
4. ONLY ONE OPTION IS CORRECT. Take approx. 2 minutes for answering each question. Q.1 Acurrentofi ampereisflowingthrough each ofthebent wiresasshown themagnitudeanddirectionof magneticfieldat0is (A)          R 2 R 1 4 i 0 (B)          R 3 R 1 4 i 0 (C)          R 2 3 R 1 8 i 0 (D)          R 3 R 1 8 i 0 Q.2 Net magneticfieldatthecentreofthecircleOduetoacurrent carrying loopas showninfigureis(<180°) (A) zero (B) perpendicularto paper inwards (C) perpendicular to paper outwards (D) is perpendicular to paper inwards if   90° and perpendicular to paper outwards if 90°<180° Q.3 The magnetic field due to a current carrying square loop of side a at a point located symmetricallyat a distance ofa/2 from its centre(as shown is) (A) a 3 i 2 0   (B) a 6 i 0   (C) a 3 i 2 0   (D) zero Q.4 AchargeparticleAof charge q = 2 C has velocityv =100 m/s.When it passes through pointAandhas velocityinthedirectionshown.ThestrengthofmagneticfieldatpointB due tothis movingcharge is(r = 2 m). (A) 2.5 T (B) 5.0 T (C) 2.0 T (D) None Q.5 Three rings,each havingequal radius R, are placed mutuallyperpendicular to each other and each having its centre at the origin of co-ordinate system. If current Iisflowingthriugheachringthenthemagnitudeofthemagneticfieldat thecommoncentreis (A) R 2 I 3 0  (B) zero (C)   R 2 I 1 2 0   (D)   R 2 I 2 3 0   Q.6 Two concentric coils X andYof radii 16 cm and 10 cm lie in the same vertical plane containing N-S direction. Xhas 20turns andcarries 16A.Yhas 25 turns &carries 18A. X hascurrent in anticlockwise direction andYhas current in clockwise direction for an observer,looking at the coils facing the west. Themagnitudeofnet magneticfield attheircommoncentreis (A) 5 × 10–4 T towards west (B) 13 × 10–4 T towards east (C) 13 × 10–4 T towards west (D) 5 × 10–4 T towards east Q.7 A uniform beam of positivelycharged particles is moving with a constant velocityparallel to another beamofnegativelychargedparticles movingwith thesamevelocityin oppositedirection separatedbya distance d. Thevariationofmagnetic fieldBalongaperpendicularlinedraw between thetwo beams is best represented by (A) (B) (C) (D)
5. Q.8 Thedimension of   where is permeability&  ispermittivityis sameas : (A)Resistance (B) Inductance (C) Capacitance (D) None of these Q.9 A current I flows around a closed path in the horizontal plane of the circle as showninthefigure.Thepathconsistsofeightarcswithalternatingradiirand2r. EachsegmentofarcsubtendsequalangleatthecommoncentreP.Themagnetic field producedbycurrent path at point P is (A) r I 8 3 0  ; perpendicular to the plane of the paper and directed inward. (B) r I 8 3 0  ; perpendicular to the plane of the paper and directed outward. (C) r I 8 1 0  ; perpendicular to the plane of the paper and directed inward. (D) r I 8 1 0  ; perpendicular to the plane of the paper and directed outward.. Q.10 InfinitenumberofstraightwireseachcarryingcurrentIareequally placed as shown in the figure.Adjacent wires have current in opposite direction.Net magnetic field atpoint P is (A) k̂ a 3 2 n 4 I 0 l   (B) k̂ a 3 4 n 4 I 0 l   (C) ) k̂ ( a 3 4 n 4 I 0    l (D) Zero Q.11 A direct current is passing through a wire. It is bent to form acoil of one turn. Now it is furtherbent to formacoiloftwoturnsbutatsmallerradius.Theratioofthemagneticinductionatthecentreofthiscoil and at the centre of the coil of one turn is (A) 1 : 4 (B) 4 : 1 (C) 2 : 1 (D) 1 : 1 Q.12 Twomutuallyperpendicularconductors carryingcurrentsI1 andI2 lieinoneplane.Locus ofthe pointat whichthemagneticinductioniszero,isa (A) circlewith centre as thepoint of intersection ofthe conductor. (B) parabolawith vertex as thepoint of intersection ofthe conductors (C)straightlinepassingthroughthepoint ofintersectionoftheconductors. (D)rectangularhyperbola Q.13 Findthe magneticfieldat P duetothearrangement shown (A)           2 1 1 d 2 i 0 (B)    d 2 i 2 0 (C)    d 2 i 0 (D)           2 1 1 d 2 i 0 Q.14 Equalcurrentiisflowinginthreeinfinitelylongwiresalongpositivex,yandzdirections.Themagnitude field at a point (0, 0, –a) would be: (A) ) î ĵ ( a 2 i 0    (B) ) ĵ î ( a 2 i 0    (C) ) ĵ î ( a 2 i 0    (D) ) k̂ ĵ î ( a 2 i 0    
6. Q.15 A thin, straight conductor lies along the axis of a hollow conductor of radius R. The two carryequal currentsinthesamedirection.ThemagneticfieldBisplottedagainstthedistancerfromtheaxis.Which ofthefollowingbest represents theresultingcurve? (A) (B) (C) (D) Q.16 A longthin walled pipe of radius R carries a current Ialong its length. The current densityisuniformoverthecircumferenceofthepipe.Themagneticfieldatthecenter of the pipe due to quarterportion of the pipe shown, is (A) R 4 2 I 2 0   (B) R I 2 0   (C) R 2 I 2 2 0   (D) None Q.17 Twoverylongstraightparallelwires,paralleltoy-axis,carrycurrents4IandI,along+ydirectionand–ydirection, respectively.Thewiresarepassesthroughthex-axisatthepoints(d,0,0)and(–d,0,0)respectively.Thegraph ofmagneticfieldz-componentasonemovesalongthex-axisfromx=–dtox=+d,isbestgivenby (A) (B) (C) (D) Q.18 Alongstraightwire,carryingcurrentI,isbentatitsmidpointtofroman angleof 45°.Inductionofmagneticfieldat pointP, distant R from pointofbendingis equal to : (A)   2 1 4 0    I R (B)   R 4 I 1 2 0    (C)   R 2 4 I 1 2 0    (D)   2 1 4 2 0    I R Q.19 Ahollowcylinderhavinginfinitelengthandcarryinguniform current perunit length  alongthecircumferenceas shown. Magneticfield insidethecylinderis (A) 2 0  (B) 0 (C) 20 (D) none Q.20 Alongstraightmetal rodhas averylongholeofradius ‘a’drilledparallel totherod axis asshown inthe figure. Ifthe rod carries acurrent ‘i’ find the value of magnetic induction on the axis of the hole, where OC = c (A)   0 2 2 ic b a ( )  (B)   0 2 2 2 ic b a ( )  (C)   0 2 2 2 i b a c ( )  (D)   0 2 2 2 ic a b Q.21 Twolongconductorsarearrangedasshownabovetoform overlapping cylinders, each of raidus r, whose centers are separated bya distance d.Current ofdensityJ flows intothe planeofthepagealongtheshaded part ofoneconductor and anequalcurrent flows out of theplane ofthe page alongthe shaded portion of the other, as shown.What are the magnitudeanddirectionofthemagneticfieldat pointA? (A) (0/2)dJ, in the +y-direction (B) (0/2)d2/r, in the +y-direction (C) (0/2)4d2J/r, in the –y-direction (D) (0/2)Jr2/d, in the –y-direction (E)Thereis no magneticfieldatA.
7. Q.22 Anelectronismovingalongpositivex-axis.Auniformelectricfieldexiststowardsnegativey-axis.What should bethedirection of magnetic fieldofsuitable magnitudesothat net forceofelectron is zero (A)positivez-axis (B)negativez-axis (C)positivey-axis (D)negativey-axis Q.23 A particle of charge q and mass m starts moving from the origin under the action of an electric field î E E 0   and î B B 0   with velocity ĵ 0 v v   . Thespeed of the particle will become 2v0 after a time (A) t = qE m 2 0 v (B) t = 0 m Bq 2 v (C) t = 0 m Bq 3 v (D) t = qE m 3 0 v Q.24 Anelectronisprojectedwithvelocityv0 inauniformelectricfieldEperpendiculartothefield.Againitis projetcedwithvelocityv0 perpendiculartoauniform magneticfieldB/ Ifr1 isinitial radiusofcurvature justafterenteringintheelectricfieldandr2 isinitialradiusofcurvaturejustafterenteringinmagneticfield then the ratio 2 1 r r is equal to (A) E Bv2 0 (B) E B (C) B Ev0 (D) E Bv0 Q.25 Auniform magnetic field ĵ B B 0   exists in a space.Aparticle of mass m and charge q is projected towards negative x-axis with speed v from the a point (d, 0, 0). The maximum value v for which the particle does not hit y-z plane is (A) dm Bq 2 (B) m Bqd (C) dm 2 Bq (D) m 2 Bqd Q.26 Two protons move parallel to each other, keeping distance r between them, both moving with same velocity V  .Thentheratio oftheelectricand magnetic force of interactionbetween them is (A) 2 2 V c (B) 2 2 V c 2 (C) 2 2 V 2 c (D) None Q.27 Achargedparticleofspecificcharge isreleased from origin attimet =0withvelocity ĵ V î V V o o    inmagneticfield î B B o   .Thecoordinatesoftheparticleattime    o B t are(specificcharge=q/m) (A)             o o o o o o B V , B V 2 , B 2 V (B)           0 , 0 , B 2 V o o (C)            o o o o B 2 V , B V 2 , 0 (D)             , B V 2 , 0 , B V o o o o Q.28 ThreeionsH+,He+ andO+2 havingsamekineticenergypassthrougharegioninwhichthereisauniform magneticfieldperpendiculartotheirvelocity,then : (A) H+ willbe least deflected. (B) He+ and O+2 will be deflected equally. (C) O+2 will be deflected most. (D)all willbedeflectedequally. Q.29 Anelectronhavingkinetic energyTismovinginacircularorbitofradius R perpendicularto auniform magneticinduction B  .Ifkineticenergyisdoubledandmagneticinductiontripled,theradiuswillbecome (A) 2 R 3 (B) 2 3 R (C) 9 2 R (D) 3 4 R Q.30 An electron (mass = 9.1 × 1031 ; charge =  1.6 × 1019 C) experiences no deflection if subjected to an electric field of 3.2 × 105 V/m anda magnetic field of2.0 ×103 Wb/m2 .Both the fields arenormal tothepathofelectron andtoeachother.Iftheelectricfieldisremoved, thentheelectronwill revolvein an orbit of radius : (A) 45 m (B) 4.5 m (C) 0.45 m (D) 0.045 m
8. Q.31 Achargedparticlemoves in amagneticfield î 10 B   withinitial velocity j ˆ 4 î 5 u    . Thepath of the particlewillbe (A)straightline (B)circle (C)helical (D) none Q.32 A electron experiences a force   j ˆ 0 . 3 î 0 . 4  × 10–13 N ina uniform magnetic field when its velocityis 7 10 k̂ 5 . 2  ms–1. When the velocityis redirected and becomes   7 10 ĵ 0 . 2 î 5 . 1   ms–1, the magnetic force of the electron iszero. Themagnetic field vector  B is: (A) – j ˆ 1 . 0 î 075 . 0  (B) j ˆ 075 . 0 î 1 . 0  (C) k̂ j ˆ 1 . 0 î 075 . 0   (D) j ˆ 1 . 0 î 075 . 0  Q.33 Amass spectrometer is a devicewhich select particle ofequal mass.An iron with electric charge q > 0 and mass m starts at rest from a source S and is accelerated through a potential differenceV. It passes through a hole into a region of constant magnetic field B  perpendicular to the plane of the paper as showninthefigure.Theparticleisdeflected bythe magneticfieldandemerges throughthebottomhole at a distance d from the top hole. The mass of the particle is (A) mV qBd (B) V 4 d qB 2 2 (C) V 8 d qB 2 2 (D) mV 2 qBd Q.34 Electronsmovingwithdifferentspeedsenterauniformmagneticfieldinadirectionperpendiculartothe field.Theywillmovealongcircularpaths. (A) ofsame radius (B)withlarger radii for thefasterelectrons (C)withsmallerradii forthefasterelectrons (D) either(B)or (C)dependingonthemagnitudeof themagneticfield Q.35 Inthe previous question, timeperiods of rotation willbe : (A)sameforall electrons (B) greater for the faster electrons (C)smaller forthefasterelectrons (D) either(B)or (C)dependingonthemagnitudeof themagneticfield Q.36 OABC is acurrent carryingsquare loop an electron is projected from the centre ofloop along its diagonalAC asshown.Unit vectorinthedirection ofinitialacceleration will be (A) k̂ (B)           2 ĵ î (C) – k̂ (D) 2 ĵ î  Q.37 A particle having charge of 1 C, mass 1 kg and speed 1 m/s enters a uniform magnetic field, having magneticinduction of 1T, at an angle=30°betweenvelocityvectorandmagneticinduction.Thepitch ofitshelicalpathis (in meters) (A) 2 3 (B)  3 (C) 2  (D)  Q.38 A charged particle is released from rest in a region of uniform electric and magnetic fields, which are parallel to eachother. Thelocus of theparticle will be (A)helixofconstantpitch (B)straightline (C)helixofvaryingpitch (D)cycloid
9. Q.39 Aparticleofspecificcharge(charge/mass)startsmovingfromtheoriginundertheactionofanelectric field î E E 0   andmagnetic field k̂ B B 0   . Its velocityat (x0, y0, 0) is ) j ˆ 3 î 4 (  . Thevalue of x0 is: (A) 0 0 B E 2 13  (B) 0 0 E B 16 (C) 0 E 2 25  (D) 0 B 2 5 Q.40 A particle of specific charge (q/m) is projected from the origin of coordinates with initial velocity [ui–vj].Uniformelectricmagneticfieldsexistintheregionalongthe+ydirection,ofmagnitudeEandB. Theparticlewilldefinitelyreturntotheoriginonceif (A) ] E 2 vB [  is an integer (B) (u2 + v2)1/2 ] E B [  is an integer (C) ] E vB [  inan integer (D) ] E uB [  is an integer Q.41 Anelectronmovingwithavelocity î 2 V1   m/satapointinamagneticfieldexperiencesaforce N ĵ 2 F1    . Iftheelectronismovingwithavelocity ĵ 2 V2   m/satthesamepoint,itexperiencesaforce N î 2 F2    . Theforcetheelectronwouldexperienceifitweremovingwithavelocity k̂ 2 V3   m/satthesamepointis (A)zero (B) N k̂ 2 (C) N k̂ 2  (D)informationisinsufficient Q.42 Two particlesof charges+Q and –Q areprojected from thesamepoint with avelocity v in aregion of uniform magnetic field B such that thevelocity vector makesan angleq with themagnetic field. Their masses are M and 2M , respectively. Then, they will meet again for the first time at a point whose distancefrom thepoint of projection is (A) QB cos Mv 2   (B) QB cos Mv 8   (C) QB cos Mv   (D) QB cos Mv 4   Q.43 A particle of charge Q and mass M moves in acircular path of radius R in a uniform magnetic field of magnitude B.The same particle now moves with the samespeed in a circular path of same radius R in thespacebetweenthecylindricalelectrodesofthecylindricalcapacitor.Theradiusoftheinnerelectrode is R/2 while that of the outer electrode is 3R/2. Then the potential difference between the capacitor electrodes must be (A) M ) 3 n ( QBR l (B) M 2 ) 3 n ( R QB 2 2 l (C) M ) 3 n ( R QB 2 2 l (D) None Q.44 A particle withcharge+Q and massm enters a magnetic fieldofmagnitude B, existingonlytotherightoftheboundaryYZ.Thedirectionofthe motionofthe particle is perpendicular to the direction of B. Let T= 2 QB m . The time spent bytheparticleinthefieldwillbe (A)T (B)2T (C) T           2 2 (D) T           2 2 Q.45 In theprevious question, if theparticlehas –Q charge, thetime spend bythe particle in thefield will be (A)T (B)2T (C) T           2 2 (D) T           2 2 Q.46 The direction of magnetic force on the electron as shown in the diagram is along (A)y-axis (B) –y-axis (C)z-axis (D)–z-axis
10. Q.47 Aparticlehavingchargeqentersaregionofuniformmagneticfield B  (directed inwards)andisdeflectedadistancexaftertravellingadistancey.Themagnitude ofthemomentumoftheparticleis: (A) 2 qBy (B) x qBy (C)          x x y 2 qB 2 (D) x 2 qBy2 Q.48 A block of mass m & charge q is released on a long smooth inclined plane magnetic field B is constant, uniform, horizontal and parallel to surface as shown. Findthetime from start when block loses contact with the surface. (A) qB cos m  (B) qB ec cos m  (C) qB cot m  (D) none Q.49 Aparticlemoving withvelocityvhavingspecificcharge(q/m)entersaregionof magneticfieldBhavingwidthd= qB 5 mv 3 atangle53°totheboundaryofmagnetic field.Findtheangle inthediagram. (A) 37° (B) 60° (C) 90° (D) none Q.50 Achargedparticleentersauniformmagneticfieldperpendiculartoitsinitialdirectiontravellinginair.The path of theparticle is seen tofollow the path infigure. Whichof statements 1–3 is/are correct? [1]Themagneticfield strengthmayhavebeen increasedwhiletheparticlewas travellinginair [2] Theparticlelost energybyionisingtheair [3] Theparticlelost chargebyionisingtheair (A) 1, 2, 3 are correct (B) 1, 2 only are correct (C) 2, 3 only are correct (D) 1 only Q.51 Astraightrodofmass mand lengthLissuspendedfrom theidenticalspringas shown inthefigure.The spring stretched bya distance of x0 due to the weight of the wire. The circuit has total resistance R. When themagneticfieldperpendiculartotheplaneofthepaperis switched on, springsare observed to extendfurtherbythesamedistance. Themagneticfieldstrength is (A) L mgR  ; directed outward from the plane of the paper (B) 0 x 2 mgR  ; directed outward from the plane of the paper (C) L mgR  ; directed into the plane of the paper (D) 0 x mgR  ; directed into the plane of the paper Q.52 A conducting wire bent in the form ofa parabola y2 = 2x carries a current i =2Aas shownin figure.This wireis placed in auniform magnetic field k̂ 4 B    Tesla.The magneticforce on the wireis (in newton) (A) î 16  (B) î 32 (C) î 32  (D) î 16
11. Q.53 A semi circular current carrying wire having radius R is placed in x-yplane with its centreat origin ‘O’. There is non-uniform magnetic field k̂ R 2 x B B o   (hereBo is+veconstant)is existingintheregion.The magneticforceactingonsemicircularwirewillbe along (A)– x-axis (B) + y-axis (C) – y-axis (D) + x-axis Q.54 A circular current loop of radius a is placedin a radial field B as shown. Thenet force acting onthe loop is (A) zero (B) 2BaIcos (C) 2aIBsin (D) None Q.55 A conductor of length l and mass m is placed along the east-west line on a table. Suddenly a certain amount ofchargeispassedthroughitanditisfoundtojumptoaheighth.Theearth’smagneticinduction is B.The charge passed throughthe conductor is: (A) 1 Bmgh (B) 2gh B m l (C) gh B m l (D) m gh B 2 l Q.56 InthefigureshownacurrentI1 isestablishedinthelongstraightwireAB.Another wire CDcarryingcurrent I2 is placed in theplaneof the paper.Theline joining theends of this wireisperpendicularto the wireAB.The forceonthewire CD is: (A) zero (B)towards left (C) directed upwards (D) none of these Q.57 Asquare loopABCD, carrying a current i, is placed near and coplanar with a long straight conductor XY carryinga current I, the net force on the loop will be (A)   3 Ii 2 0 (B)   2 Ii 0 (C)   3 Ii 2 0 l (D)   2 Ii 0 l Q.58 A metal ringof radius r =0.5 m with its plane normal to a uniform magnetic field B ofinduction 0.2 T carries acurrent I= 100A.The tension in newtons developed in the ring is: (A) 100 (B) 50 (C) 25 (D) 10 Q.59 Ingivenfigure,XandYaretwolongstraight parallelconductorseach carrying a current of 2A.The force on each conductor is F newtons. When the current in each is changed to 1Aand reversed in direction, the force on each is now (A) F/4 andunchangedin direction (B) F/2 andreversed in direction (C)F/2 andunchangedindirection (D) F/4 and reversed in direction Q.60 A conductingringof mass 2kgand radius 0.5m is placedona smooth horizontal plane. The ring carries a current i = 4A.Ahorizontal magnetic field B = 10T is switched onat timet =0 as shownin figure. Theinitial angularacceleration of theringwillbe (A) 40  rad/s2 (B) 20  rad/s2 (C) 5  rad/s2 (D) 15  rad/s2 Q.61 InthefigureshownacoilofsingleturniswoundonasphereofradiusRandmass m. The planeof thecoil is parallel to the planeand lies intheequatorial plane of the sphere. Current in the coil is i. Thevalue of B ifthe sphere is in equilibrium is (A) iR cos mg   (B) iR mg  (C) iR tan mg   (D) iR sin mg  
12. Q.62 Themagneticmomentofacircularorbit ofradius‘r’carryingacharge ‘q’androtating with velocityvis givenby (A)  2 qvr (B) 2 qvr (C) qvr (D) qvr2 Q.63 Thedimensionalformulaforthephysicalquantity 2 0 0 2 B E   is (E=electric fieldand B=magnetic field) (A) L0M0T0 (B) L1M0T–1 (C) L–1M0T1 (D) L1/2M0T–1/2 Q.64 AthinnonconductingdiscofradiusRisrotatingclockwise(seefigure)withanangularvelocitywabout itscentralaxis,whichisperpendiculartoitsplane. Bothitssurfacescarry+vechargesofuniformsurface density.Halfthediscisinaregionofauniform,unidirectionalmagneticfieldBparalleltotheplaneofthe disc, as shown. Then, (A) The net torque on the disc is zero. (B) The net torque vector on the discis directed leftwards. (C) The net torque vector on the disc is directedrightwards. (D) The net torque vector on the disc is parallel to B. Q.65 A rectangular coil PQ has 2n turns, an area 2a and carries a current 2I, (refer figure). Theplaneofthecoilis at 60° toa horizontal uniformmagneticfield of flux densityB.Thetorque onthe coil due to magnetic force is (A) BnaI sin60° (B) 8BnaI cos60° (C) 4naI Bsin60° (D) none Q.66 Astraightcurrentcarryingconductorisplacedinsuchawaythatthecurrentintheconductorflowsinthe direction out of the plane of the paper.The conductor is placed between two poles of two magnets, as shown. Theconductor willexperiencea force inthe directiontowards (A) P (B) Q (C) R (D) S Q.67 Figure shows a square current carryingloopABCD of side 10 cm and current i=10A.Themagneticmoment M  oftheloopis (A) (0.05)   2 m A k̂ 3 î   (B) (0.05)   2 m A k̂ j ˆ   (C) (0.05)   2 m A k̂ î 3   (D)   2 m A k̂ î   ONE OR MORE THAN ONE OPTION MAY BE CORRECT Take approx. 3 minutes for answering each question. Q.1 In the followinghexagons, made up oftwo different material P and Q, current enters and leaves from points X andYrespectively. Inwhich case the magneticfield at its centreis not zero. (A) (B) (C) (D) Q.2 Considerthemagneticfieldproducedbya finitelylongcurrentcarryingwire. (A)the linesoffieldwill beconcentriccircles with centreson thewire. (B) There can be two points inthe same plane where magneticfields are same. (C) There can be largenumberofpoints where the magneticfield is same. (D)Themagneticfield atapointisinversallyproportional tothedistanceofthepointfromthewire.
13. Q.3 Consider three quantities x = E/B, y = 0 0 / 1   and z = CR l . Here, l is the length of a wire, C is a capacitance andR is a resistance.All other symbols havestandard meanings. (A)x, yhavethesame dimensions (B)y, zhavethe samedimensions (C)z, xhavethesame dimensions (D)none ofthe three pairs havethe same dimensions. Q.4 Twolongthin,parallelconductorscarryingequalcurrentsinthe samedirectionarefixedparalleltothex-axis,onepassingthrough y=aandtheotherthroughy=–a. Theresultant magnetic field due to the two conductors at any point is B. Which of the followingarecorrect? (A) B = 0 for all points on the x-axis (B)At all points on they-axis,excludingthe origin, B hasonlya z-component. (C)At allpoints on the z-axis, excluding the origin, Bhasonlya y-component. (D) B cannot have an x-component. Q.5 Currentflows throughuniform,squareframesasshown. Inwhichcaseisthemagneticfieldatthecentre of theframe not zero? (A) (B) (C) (D) Q.6 Awire carryingIis shapedas shown. SectionAB is a quartercircle ofradius r.The magneticfield at C is directed (A) alongthe bisector of the angleACB, awayfromAB (B) alongthe bisector of the angleACB, towardsAB (C) perpendicular to the plane of the paper, directed into the paper (D) at an angle /4 to the plane of the paper Q.7 A long straight wire carries a current along the x-axis. Consider the points A(0, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(1, 1, 1). Which of the following pairs of points will have magnetic fields of the same magnitude? (A)Aand B (B)Aand C (C) B and C (D) B and D Q.8 In the previous question,if the current is i andthe magneticfield at Dhasmagnitude B, (A) B =   2 2 i 0 (B) B =   3 2 i 0 (C) B is parallel to the x-axis (D) B makes an angle of 45° with the xyplane Q.9 Whichofthefollowingstatementiscorrect: (A)Achargedparticleentersaregionofuniformmagneticfieldatanangle850 tomagneticlinesofforce. The pathof the particle is a circle. (B)Anelectronandprotonaremovingwiththesamekineticenergyalongthesamedirection.Whenthey passthroughuniformmagneticfieldperpendiculartotheirdirectionofmotion,theydescribecircular path. (C)Thereisnochangeintheenergyofacharged particlemoving inamagneticfield although magnetic force acts on it. (D)Twoelectrons enterwiththesame speed but in oppositedirection in auniform transverse magnetic field. Then the two describe circleof the same radius and these move in the same direction.
14. Q.10 Twoidenticalchargedparticlesenterauniformmagneticfieldwithsamespeedbutatangles30°and60° with field. Let a, b and cbe the ratio oftheir time periods, radii and pitches of thehelical paths than (A) abc = 1 (B) abc > 1 (C) abc < 1 (D) a = bc Q.11 Considerthefollowingstatementsregardingachargedparticleinamagneticfield.Whichofthestatements are true : (A) Starting with zero velocity, it accelerates inadirectionperpendicular tothe magneticfield. (B)Whiledeflectinginmagneticfielditsenergygraduallyincreases. (C) Only the component of magnetic field perpendicular to the direction of motion of the charged particleiseffectiveindeflectingit. (D)Directionofdeflectingforceon themovingcharged particle is perpendicularto its velocity. Q.12 A particle ofcharge q and velocityv passes undeflected througha space with non-zeroelectric field E andmagneticfieldB.Theundeflectingconditionswillholdif. (A) signs of both q and E are reversed. (B) signs of both q and B are reversed. (C) both Band E are changed in magnitude, but keepingthe product of |B|and |E|fixed. (D) bothB and E aredoubled in magnitude. Q.13 Two charged particle A and B each of charge +e and masses 12amuand13amurespectivelyfollowacirculartrajectoryinchamber X after the velocity selector as shown in the figure. Both particles enter the velocity selector with speed 1.5 × 106 ms–1. A uniform magneticfieldofstrength1.0Tismaintainedwithinthechamber X and inthevelocityselector. (A) Electric field across the conducting plate of the velocityselector is – 106 NC–1 î . (B) Electric fieldacross the conducting plate of the velocityselector is 106 NC–1 î . (C) The ratio B A r r of the radii of the circular paths for the two particles is 13 12 . (D) The ratio B A r r ofthe radii ofthe circular paths for the two particles is 12 13 . Q.14 An electronis movingalongthepositive X-axis.You wanttoapplya magneticfield fora short time so that the electronmayreverseitsdirection andmoveparalleltothenegativeXaxis.Thiscanbedoneby applyingthemagneticfieldalong (A)Y-axis (B) Z-axis (C)Y-axis only (D) Z-axis only Q.15 Inaregionofspace,auniform magneticfieldBexistsinthey-direction.Aproton is fired from theorigin, withits initial velocityvmakingasmall anglewith the y-direction in theyz plane. Inthe subsequent motion ofthe proton, (A) its x-coordinatecanneverbe positive (B) its x- and z-coordinates cannot both be zero at the same time (C) its z-coordinatecan never be negative (D) its y-coordinatewill be proportional tothe squareof itstime offlight Q.16 ArodABmoveswithauniformvelocityvinauniform magneticfieldasshowninfigure. (A) The rod becomes electricallycharged. (B)The endAbecomes positivelycharged. (C) The endB becomes positivelycharged. (D) The rod becomes hot because of Joule heating.
15. Question No. 17 to 21 (5 questions) The followingexperiment was performed byJ.J.Thomsonin order to measure the ratio of the chargeetothemassm ofanelectron.FigureshowsamodernversionofThomson'sapparatus.Electrons emittedfrom ahotfilament areacceleratedbyapotential differenceV.As theelectronspass throughthe deflector plates, theyencounter both electric andmagnetic fields. When the electrons leave the plates they enter a field-free region that extends to the fluorescent screen. The beam of electrons can be observedasaspotoflightonthescreen.Theentireregioninwhichtheelectronstravelisevacuatedwith avacuumpump. Thomson's procedure was to first set both the electric and magnetic fields to zero, note the position oftheundeflectedelectron beam onthescreen,thenturn on onlytheelectricfield and measure the resulting deflection. The deflection of an electron in an electric field of magnitude E is given by d1=eEL2/2mv2, where Lis the length of the deflecting plates, and v is the speed of the electron. The deflection d1 can alsobe calculated from the total deflection of the spot on the screen, d1 + d2 and the geometryoftheapparatus.Inthesecondpartoftheexperiment,Thomsonadjustedthemagneticfieldso as toexactlycancel the force applied bythe electricfield, leaving the electronbeam undeflected. This gives eE =evB. Bycombining this relation with the expression for d1, one can calculate the charge to mass ratio oftheelectronas afunction oftheknownquantities.The result is: 2 2 1 L B E d 2 m e  Q.17 Whywas itimportant forThomson toevacuatetheair from theapparatus? (A) Electrons travel faster in a vacuum, making the deflectiond1 smaller. (B)Electromagneticwavespropagateina vacuum. (C)Theelectroncollisionswiththeairmoleculescause them to be scattered, and a focusedbeam will not be produced. (D) It was not important and could have been avoided. Q.18 Onemighthave considereda different experiment in which no magnetic field is needed.The ratio e/m can then be calculated directlyfrom the expression for d1. Whymight Thomson have introduced the magneticfieldBinhisexperiment? (A)To verifythe correctness ofthe equation for themagnetic force. (B)To avoidhavingto measure theelectron speed v. (C)To cancel unwanted effects of theelectric field E. (D)To make sure that the electric field does not exert a force on the electron. Q.19 IftheelectronspeedweredoubledbyincreasingthepotentialdifferenceV,whichofthefollowingwould have to be true in order to correctlymeasure e/m? (A)Themagneticfieldwouldhavetobecutinhalfinordertocanceltheforceappliedbytheelectricfield. (B)Themagneticfield wouldhaveto bedoubledinordertocanceltheforceappliedbytheelectricfield. (C) The length of the plates, L, would have to be doubled to keep the deflection, d1,from changing. (D) Nothing needs to be changed. Q.20 ThepotentialdifferenceV,whichacceleratestheelectrons,alsocreatesanelectricfield.WhydidThomson NOTconsiderthedeflectioncaused thiselectricfieldin hisexperiment? (A)This electricfield is muchweakerthan the one betweenthe deflectingplates and can be neglected. (B) Onlythe deflection, d1 + d2 caused bythe deflecting plates is measuredin the experiment. (C)Thereisnodeflectionfromthis electricfield (D) Themagneticfield cancels theforcecausedbythiselectricfield.
16. Q.21 Iftheelectronisdeflecteddownwardwhenonlytheelectricfieldisturnedon(asshowninfigure)thenin what directions do theelectricandmagnetic fields point inthe second part ofthe experiment? (A)Theelectricfield points tothebottom, whilethemagnetic field points into thepage. (B) Theelectricfield points tothebottom, whilethe magneticfield points outof thepage. (C) The electricfield points tothetop, whilethemagnetic fieldpoints intothepage. (D)Theelectric field points tothe top, while themagnetic fieldpoints outof the page. Q.22 AconductorABCDE, shaped as shown, carries a current i. It is placed in the xyplane with the endsA andEonthex-axis.Auniform magneticfieldofmagnitudeBexists intheregion.Theforceactingon it willbe (A)zero,ifB is inthe x-direction (B)Bi in thez-direction, ifB isinthe y-direction (C)Bi inthenegativey-direction, if Bisin the z-direction (D)2aBi, ifBis inthex-direction Q.23 Asquareloopofsideisplacedintheneighbourhoodofaninfinitelylongstraightwirecarryingacurrent I1. The loop carries a current I2 as shown in figure (A)Themagnetic moment of theloop is k̂ I p 2 2 m l   (B)Themagneticmoment of theloop is k̂ I p 2 2 m l    (C)Thepotentialenergyoftheloopisminimum (D) Thetorqueexperiencedbytheloopis maximum Q.24 The magnetic dipole m p  is placedparallel to an infinitelylongstraight wireas showninfigure (A)thepotentialenergyofthedipoleisminimum (B) the torque acting on the dipole is zero (C) the force acting on thedipole is zero (D) none of these ANSWER KEY ONLY ONE OPTION IS CORRECT. Q.1 D Q.2 C Q.3 C Q.4 A Q.5 A Q.6 A Q.7 D Q.8 A Q.9 A Q.10 B Q.11 B Q.12 C Q.13 A Q.14 A Q.15 B Q.16 A Q.17 C Q.18 A Q.19 B Q.20 B Q.21 A Q.22 B Q.23 D Q.24 D Q.25 B Q.26 A Q.27 D Q.28 B Q.29 C Q.30 C Q.31 C Q.32 A Q.33 C Q.34 B Q.35 A Q.36 B Q.37 B Q.38 B Q.39 C Q.40 C Q.41 A Q.42 D Q.43 C Q.44 C Q.45 D Q.46 A Q.47 C Q.48 C Q.49 C Q.50 B Q.51 A Q.52 B Q.53 A Q.54 C Q.55 D Q.56 D Q.57 A Q.58 D Q.59 A Q.60 A Q.61 B Q.62 B Q.63 A Q.64 B Q.65 B Q.66 B Q.67 A ONE OR MORE THAN ONE OPTION MAY BE CORRECT Q.1 A Q.2 A,B,C Q.3 A,B,C Q.4 A,B,C,D Q.5 C Q.6 C Q.7 B,D Q.8 A,D Q.9 B,C Q.10 A,D Q.11 C,D Q.12 D Q.13 C Q.14 A,B Q.15 A Q.16 B Q.17 C Q.18 B Q.19 A Q.20 C Q.21 D Q.22 A,B,C Q.23 A Q.24 C
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