MAGNETICS EFFECTS OF ELECTRIC CURRENT

Transcription

1 Lesson- MAGNETCS EFFECTS F ELECTC CUENT este in 8 by obseving the eflection of compass neele when it is bought nea a cuent caying conucto iscovee that a cuent caying conucto pouces magnetic fiel in space suouning it. This fiel is escibe by vecto calle magnetic inuction, flu ensity o simply fiel vecto with units Wb/m o tesla. n case of cuent caying conucto it is compute eithe with the help of iot-savat law o Ampee s law. iot Savat law is magnetic analogue of Coulomb s law while Ampee s law is analogous to Gauss s law. T-SAVAT LAW This law povies a metho fo calculating the magnetic inuction at any point in space aoun a conucto caying a cuent. f a small element of length l of a long conucto caies a cuent, the magnetic fiel o magnetic inuction at any point P at a istance is given by iot-savat law as μ l 4π Hee is the position vecto of the point P fom the cente of the element of length l. f is the angle which P makes with the length of small element of the conucto, the magnitue of magnetic inuction is given by = l( sin θ) 4 = l(sin θ) 4 whee is the pemeability of fee space an ( l = l sin ) l P 4 7 Webe/ampee/mete The iection of is pepenicula to the plane of line tangential to the cuent element l an aius vecto which joins l to P. The total magnetic inuction fo the conucto, Webe/mete o tesla.. The unit of magnetic inuction is Tesla = Webe / mete = Newton / ampee mete. The magnetic intensity H at any point in the magnetic fiel is elate to the magnetic inuction as

2 H o = H whee is pemeability of the meium. The unit of magnetic intensity H is ampee / mete. Mawell s Cok Scew ule: f a ight hane cok scew is otate so that its tip moves in the iection of flow of cuent though the conucto, then the iection of otation of the hea of the scew gives the iection of magnetic lines of foce. ight Han ule :f the conucto is hel in the ight han such that the thumb points in the iection of the cuent, the iection in which the finges cul gives the iection of the magnetic fiel. APPLCATNS F T-SAVAT LAW. Magnetic nuction ue to Long Staight Cuent Caying Conucto : Consie the cuent flowing though a long cuent caying conucto. f a small element CD of the conucto has a length l, then the fiel at P ue to this conucto is given by iot-savat law as : = l sin 4 whee is the istance between the cuent element CD an point P an is the angle between CD an line joining it with the point P. The total magnetic fiel is given by DE f DE is CD, then in CDE, sin = CD l = DE sin l sin 4 C D E P = 4 DE sin sin 4 DE As CPD = = DE o DE = Also in PD, cos o cos = 4 4 cos = cos...(i) 4 The magnetic inuction fo iffeent lengths of conuctos can be foun fom equation (i) as follows :

3 (i) A conucto of infinite length : n this case, vaies fom the mile point of conucto, to, when point P lies on 4 π π cos (ii) A conucto of finite length : f the conucto subtens an angle above hoizontal line P an below P fo finite length EF of the conucto, 4 cos 4 4 = sin [sin sin ] (iii)at the en of a conucto of infinite length : Hee is angle is /, π cos 4 4 (iv) At one en of a conucto of finite length : Angle is an angle = 4 cos sin 4 (v) f point P lies along length of the conucto, then at P is zeo.. Magnetic Fiel on the Ais of a Cuent Caying Cicula Coil : f a cuent is flowing in a cicula coil of aius an cente, then the stength of the magnetic fiel ue to an element AC of length l at the cicumfeence of the coil at a point P on its ais at a istance is given by iot- Savat Law as : l whee is 4 l A C Y a vecto fom C to P. The iection of at P is pepenicula to the line P X joining P to AC. As the angle between l an is 9º, can be esolve into one ectangula compoun cos along PY an anothe ectangula component sin along PX. As thee is a symmetical element A' C' on the lowest potion of the coil which will have fiel of equal to magnitue at P which can be esolve into a ectangula component cos along PY' an a ectangula component sin along PX, As the components of fiel along PY an PY' ae equal in magnitue an opposite in iection, these cancel each othe fo all such symmetical elements. The esultant fiel is theefoe along the ais of the coil an it is given by :

4 = sin 4 sin l As l 4, sin = 4 = l = ) ( (i) f the coil has n tuns of the coil, ) ( n (ii) The fiel at cente of the coil with equal to zeo = = n n (iii) f the point P is at a vey lage istance fom the coil an >>, = n f A is aea of one tun of the coil, A = A n A cicula loop caying cuent behaves like a magnetic ipole place along the ais of the coil. S N f the cuent in one of the faces appeas flowing in clockwise iection, it behaves as a south pole an if the same face is obseve fom the opposite sie, the cuent flows on this face in an anticlockwise iection which behaves as a noth pole.. Magnetic Fiel Due to Cicula ac: Consie a cuent flowing though a cicula ac wie of aius. The magnetic fiel pouce by the cuent though element l at point C fom iot Savat law is : 4 sin 4 4 l l l C l sin l l

5 The magnetic inuction ue to cicula ac = Fo semicicula loop = l = 4 The iection of in case of cicula cuent caying conuctos o cuent caying close loop can be calculate as follows: f the iection of cuent coincies with the iection of the cul of finges of ight han, the stetche thumb points in the iection of fiel insie loop. 4. Magnetic Fiel nsie a Cuent Caying Solenoi : A lage numbe of tuns of insulate wie can be woun in the fom of heli on a long cylinical fame which is known as a solenoi. When a cuent is passe though such a solenoi, the magnetic fiel is pouce insie as well as outsie the solenoi. S N iot-savat law can be use to calculate the magnetic fiel at any point ue to the cuent flowing in a solenoi. f a cuent is flowing in a solenoi of n tuns, then the magnetic fiel pouce by this cuent at a point P on the ais, ue to the cuent though the potion of the solenoi lying between angle an + w..t. ais PD, is obtaine by using iot-savat Law. Consie an element A of coil of with locate at a istance fom the point whee the magnetic fiel ue to solenoi is to be measue. Let n be numbe of tuns pe unit length. The magnetic fiel at point P ue to elementay coil is Ni n i = ( ) ( ) whee total numbe of tuns, N = n fo the element. n P, = cot, = cosec C P A D X ni ( cosec / ) = ( cot ) = ni cosec cosec = n i sin f the ens of the solenoi D an C subten angles an with espect to the positive iection PX of the ais of the solenoi, then the net magnetic fiel at P on the ais ue to the solenoi is

6 n θ θ sin n θ cos θ n cos cos f the solenoi is of infinite length, =, = 8º n n ( ) n The magnetic fiel at the en of last tun fo = 9º an = 8 is given by n n ( ) The magnetic fiel at the en of the fist tun fo = an = 9 is n n FCE N A CHAGED PATCLE N MAGNETC FELD f a paticle of chage q tavels with a velocity v in a unifom magnetic fiel, it epeiences a foce F calle as the Loentz foce given by F = q(v ) F = q v sin The iection of F is pepenicula to that of v an. Thus if the magnetic fiel is acting along y-ais on chage +q moving with velocity v in y plane making an angle with the iection Y v of, the chage paticle epeiences a Loentz Foce F along z ais which is mutually pepenicula to an v. +q X q F v sin Z F = q ( v ) f q = coulomb, v = m/s sin = fo = 9º, F = Newton = Testla = Webe / m Thus tesla is efine as the unit of magnetic fiel stength in S.. units which when acting on one coulomb of chage moving with a velocity of m/s at ight angles to the magnetic fiel eflects it with a foce of newton in a iection pepenicula to that of fiel an velocity vectos. C.G.S. unit of magnetic fiel stength o magnetic inuction is gauss o este. gauss = oeste = 4 tesla.

7 Tajectoy of a chage paticle in a Magnetic Fiel (i) f the iection of v of chage paticle is paallel ( = ) o antipaallel ( = 8º) to, F =, the tajectoy of a paticle is a staight line. (ii) (iii) f v is pepenicula to i.e. = 9º, F = qv an the iection of this maimum foce is always pepenicula to v. The tajectoy of the chage paticle is a cicula path. f the paticle makes an angle with the fiel which lies between º an 9º, the paticle moves in a heli ue to the component v sin which is pepenicula to an makes the chage paticle move along a cicula path wheeas the component v cos, which is paallel to, makes it move along a staight line with the esult that the chage paticle moves along a helical path ue to the supeposition of two motions. f a paticle of mass m an chage q moves in a magnetic fiel with spee v in a cicula path, the magnetic foce povies the centipetal foce. qv = mv o q ω v m q Fequency f =, time peio = T = m T is inepenent of v. m q f a paticle with chage q moves with a spee v whee both the electic fiel E an magnetic fiel ae pesent, the esultant foce F is given by F = q(e + v ) Foce on a cuent Caying Conucto in a Magnetic Fiel: Though epeiments Ampee establishe that when a cuent element of length l is place in magnetic fiel, it epeiences a foce F = l, whee is cuent though the element f l an ae incline at an angle with each othe, F = l sin. f is unifom ove the length of the conucto, F = ( L ) F = L sin whee L is the length of the conucto. The iection of foce (which is given by Fleming s left han ule) is always pepenicula to the plane containing the conucto an the magnetic fiel. Z F Y L X

8 Fleming s Left Han ule: f the left han is stetche in such a manne that the thumb an the fist two finges of the left han ae stetche mutually pepenicula to each othe an if the fist finge is pointe in the iection of the fiel an the secon (mile) finge is pointe in the iection of the cuent, then the iection of thumb gives the iection of foce. Foce Fiel Cuent Magnetic Foce between Two Long Paallel Cuent Caying Conuctos: Any cuent caying conucto pouces a magnetic fiel aoun it. f anothe cuent caying conucto is place nea the fist one, the secon conucto will epeience a foce ue to magnetic fiel pouce by the fist conucto. Similaly, the fist conucto will epeience a foce ue to the magnetic fiel pouce by the secon conucto. Thus both cuent caying conuctos eet foce on each othe ue to the effects of thei magnetic fiels. The conuctos attact each othe if thei cuents ae in the same iection an these epel each othe if thei cuents ae in opposite iection. P F F F f thee ae two long paallel staight cuent caying conuctos P an Q place at a istance fom each othe in the plane of the pape so that the espective cuents an ae flowing though these. The magnetic fiel at Q ue to conucto P = = The iection of is pepenicula to Q an plane of pape insie. The foce acting pe unit length of conucto is F N/m Similaly the foce acting pe unit length F on conucto P ue to the cuent is F N/m The magnetic foce F between two paallel cuent caying conuctos pe unit length is F N/m f = m, = = ampee, F = 7 N.

9 ne ampee is efine as that steay cuent which when flowing though each of two infinitely long staight paallel wies place m apat in vacuum pouces a foce of 7 N pe mete of length epeience by each wie. Effect of Magnetic Fiel on a Cuent Loop : Consie a ectangula loop PQS having N tuns, length l, beath b an aea A place in a unifom magnetic fiel in such a way that the nomal to the coil subtens an angle to the iection of when a cuent flows though the loop clockwise. The sies PQ an S ae pepenicula to the fiel an equal an opposite foces of magnitue l act upwas an ownwas espectively. An equal an opposite foce acts on sies l P S i b Q Q & PS towas ight an left of coil. The esultant foce is zeo but the esultant toque is not zeo. The foces on sies PQ an S pouce a toque ue to a single tun which is given by = lb sin = A sin ( A = l b) f thee ae N tuns of simila loops in the coil, = NA sin = M sin. Whee M = NA When = º, = when the plane of the coil is pepenicula to the fiel. is maimum when = 9º, the plane of the coil is paallel to the fiel i.e. = NA Magnetic Dipole Moment : Compaing the above esult with the toque epeience by a ba magnet of magnetic moment M, place in a magnetic fiel ( = M ), we conclue that a cuent caying loop behaves like a ba magnet of magnetic moment A, whee A is the aea of the loop. Fo a cuent caying coil of N tuns, the coesponing magnetic moment will be NA. The unit of magnetic moment is ampee.mete. The potential enegy U of a magnetic ipole place in a magnetic ipole is U = M cos o U = M The magnetic fiel at a lage istance on the ais of a ipole of magnetic moment M is M = 4 The magnetic fiel at a lage istance on the equatoial line of a ipole of magnetic moment M is M = 4 egaing the foce on cuent caying conucto in magnetic fiel thee ae some impotant points given below:. As the foce L sin is not a function of position, the magnetic foce on a cuent element is non-cental (a cental foce is of the fom F = Kf ()n ) M

10 . The foce F is always pepenicula to both an L though an L may o may not be pepenicula to each othe.. n case of cuent-caying conucto in a magnetic fiel foce acting, F = L L (if magnetic fiel is unifom i.e., = constant) an as fo a conucto L epesents the vecto sum of all the length elements fom initial to final point, which in accoance with the law of vecto aition is equal to the length vecto L joining initial to final point, so a cuentcaying conucto of any abitay shape in a unifom fiel epeiences a foce F = L = L whee L is the length vecto joining initial an final points of the conucto as shown in the figue. L A F = L 4. f the cuent-caying conucto in the fom of a loop of any abitay shape is place in a unifom fiel, L L F = an as fo a close loop, the vecto sum of L is always zeo. So, F = [as L = ] i.e., the net magnetic foce on a cuent loop in a unifom magnetic fiel is always zeo as shown in figue. F L Hee it must be kept in min that in this situation iffeent pats of the loop may epeience elemental foce ue to which the loop may be une tension o may epeience a toque as shown below: F out F = F = F in F = = Cuent loop in a unifom feil F = 5. f a cuent-caying conucto is situate in a non-unifom fiel, its iffeent elements will epeiements iffeent foces; so in this situation, F but may o may not be zeo. f the conucto is fee to move, it tanslates with o without otation as shown below

11 A A D F F D F F C C F F = Loop in the fiel of cuent caying wie A A cuent caying o in the fiel of wie A 6. n case of a cuent-caying conucto in a magnetic fiel if the conucto epeience a foce an is fee to move, wok will be one an hence its kinetic enegy will change, i.e., W = KE with W = F s. (Though F = i ( l) but eal enegy is supplie by battey as magnetic foce oes no wok) MVNG CL GALVANMETE t is base on the pinciple that when a cuent caying coil is place in a unifom magnetic fiel, it epeiences a foce an a toque is pouce which eflects the coil accoing to Fleming s left han ule an the cuent though the coil is popotional to the eflection of the coil. n a moving coil galvanomete, the coil is suspene between the cuve pole pieces of a hose-shoe type magnet. The pole pieces ae mae cylinical an a soft ion cylinical coe is place within the coil without touching it which makes the fiel aial. n such a fiel, the plane of the coil is always paallel to the fiel such that the nomal to the coil subtens an angle equal to 9º with the iection of. The toque eflecting the coil is given by = NA Scale N Magnet CE CL S As the coil eflects, a estoing toque is pouce eithe in the suspension fibe o the sping, to which the pointe is attache. f is the angle of twist, the estoing toque = C, whee C is the estoing toque pe unit twist. n equilibium position, NA = C. C NA θ Kθ

12 C Whee = K is a constant of the galvanomete. As the cuent is iectly popotional to the eflection NA, the scale of the galvanomete can be calibate to etect as well as measue small amounts of cuents in milliampees (ma) o in micoampees ( A). A galvanomete is sai to be sensitive if it gives a lage eflection fo a small cuent. The cuent sensitivity of a galvanomete is the eflection of galvanomete pe unit cuent. t is given by NA C Voltage sensitivity of a galvanomete is eflection of galvanomete pe unit voltage. t is given by V o NA V C A galvanomete can be convete into an ammete by using a low esistance wie (shunt) in paallel with the galvanomete. n figue, fo potential iffeence V, galvanomete G of esistance g an capable of measuing a smalle cuent g can be convete into an ammete capable of measuing a lage cuent by connecting a small esistance s in paallel calle as the shunt esistance such that g g s G s g g g Also, such a galvanomete can be convete into a voltmete of ange V volts by connecting a high esistance in seies whose value is given by g V g g A G V

13 SLVED EXAMPLES E. A cuent of one ampee is flowing along the sies of an equilateal tiangle of sie 4.5 m. Fin the magnetic fiel at the centoi of the tiangle. P Sol.: Consie an equilateal tiangle PQ of each sie. The magnetic fiel at the centoi ue to cuent flowing along one sie of the tiangle is whee A = (sin sin ) 4 The esultant magnetic fiel at ue to all sies of the tiangle is Q A (sin sin ) 4 Fo all the sies of PQ, = = 6º, = A A = = cot m = = 4 5 Tesla. E. The centes of two simila coils P an Q having same numbe of tuns ae locate at cooinates (.4, ) m an (,.) m such that the plane of coils ae pepenicula to X an Y aes espectively. The aeas of coss sections of coils P an Q ae in the atio 4 :. The coil P has 6 A cuent in clockwise iection an the coil Q has 9 A cuent in anticlockwise iection as seen fom the oigin. A small compass neele is place at the oigin. Fin the eflection of the neele assuming the eath s magnetic fiel negligible an the aii of the coils vey small as compae to thei istances fom the oigin. (Take aius of ing is small) Sol.: The magnetic fiel on the ais of a cuent caying coil of aius an N numbe of tuns at a istance fom the cente of coil is given by N = ( ) N A = ( ) = ( N( ) ) Y Q P P X whee A = aea of coil an = cuent Q N A When <<, =

14 N P A Magnetic fiel at ue to coil P = P = N Q A Magnetic fiel at ue to coil Q = Q = y P Q along X along Y' whee P, A P an Q, A Q ae espective cuents an aeas of coils P an Q espectively. f the compass neele makes an angle with -ais, (magnetic neele aligns itself along the iection of net magentic fiel) Q Q A Q tan P P A P y = 6º 9.4 = 6 4. E.. Sol. A solenoi of length.4 m an iamete.6 m consists of a single laye of tuns of fine wie caying a cuent of 5. milliampee. Fin the magnetic fiel on the ais at the mile an at the ens of a solenoi. The magnetic fiel insie a cuent caying solenoi at any point lying on the ais is given by n = (cos cos ) whee n is the numbe of tuns pe unit length an is the cuent an an ae angles subtene by the ens of solenoi with espect to the positive iection of -ais. At the mile of the solenoi, cos = cos = cos ( ) = cos =.5547 (.). (.).5547 At, = ( ) = tesla.4 At one en of the solenoi, cos. 8 (.) (.) = 9 cos =

15 .4m E.4. At A, = 4 = tesla A poton of mass.6 7 kg an chage.6 9 C entes a egion of unifom magnetic fiel of stength tesla along the iection shown in the figue such that its spee is 7 m/s. (i) (ii) f the magnetic fiel is iecte along the inwa nomal to the plane of the pape an the paticle leaves the egion of the fiel at the point F, fin the istance EF an the angle. f the iection of the magnetic fiel is along the outwa nomal to the plane of the pape, fin the time spent by the paticle in the egion of magnetic fiel afte enteing at E. 45º F E Sol. (i) f the iection of the magnetic fiel is iecte along the inwa nomal to the plane of the pape, the path of the paticle is an ac of a cicle of aius = E = F. As m v q v, = EF = sin 45º. mv q =.m 9.6 EF =. =.4 m, = 45 9º F 9º E A C (ii) f the iection of the magnetic fiel is iecte along the outwa nomal to the pape, the path ECH of the paticle in the egion of magnetic fiel will be a cicula one with aius an cente at. n the figue, EH = 9 F Length of ac = ECH = Time spent by the paticle along the ac ECH in the magnetic fiel = v A E 45º 45º H C.4. = 7 = sec.

16 E.5. A beam of potons having a velocity of 4 5 metes pe secon entes a unifom magnetic fiel of. tesla at an angle of 6º to the magnetic fiel. Fin the aius of the helical path taken by the poton beam. Fin the time peio of otation an pitch of the heli. Sol. The component of velocity v of potons paallel to the magnetic fiel = v = v cos 6 = 4 5 = 5 m/s The component of velocity pepenicula to the magnetic fiel = v = v sin 6 = 4 5 = m/s aius of the heli = = = mv q.67 The time peio of otation = T = =. m =. cm m q 5 v 6 v v = v cos 6 T = =.85 7 sec. Pitch of the heli = v T = = 4.7 m E.6. A wie ACDEF (with each sie of length L) is bent as shown in the figue an is caying cuent in a unifom magnetic inuction paallel to the y-ais. What is foce epeience by wie. z D C E F y Sol. A f Point A is joine to point F by conucting wie, it becomes a close loop. No foce acts on close loop when place in unifom magnetic fiel, F ACDEFA = f F is foce on given netwok an F on wie AF F + F = whee F = L along negative z-ais F = L along positive z-ais. C z E D A F y

17 E.7. Sol. A chage Q is spea unifomly ove an insulate ing of aius. What is the magnetic moment of the ing if it is otate with an angula velocity with espect to the nomal ais. A chage in motion constitutes cuent. Evey element of this ing caying a chage q pouces cuent = q fequency with which it goes oun the loop. Theefoe, chage on element l of the ing is, q = Q l Cuent ue to cicula motion of this chage = Q l Magnetic moment, M = A = Q M = l 4 Q l 4 = Q Altenatively, a chage Q going oun a loop with angula velocity is equivalent to a cuent = Q The magnetic moment of the loop = A = Q = Q. E.8. Sol. What is the value of shunt which passes % of the main cuent though a galvanomete of 99 ohm? As shunt is a small esistance S in paallel with a galvanomete (of esistance G) as shown in figue. i.e., S = ( G )S = G G GG ( ) G ( ) G S An as hee, G = 99 an G = =. G G. 99. S = 99 (.).9 = E.9. f a shunt of value (/n) times the galvanomete esistance is applie to a moving coil galvanomete, by what facto will its cuent sensitivity will change? Sol. f an ae the eflections in a galvanomete an shunte galvanomete ue to cuent, flowing though them, then CS = an CS =

18 Now as in case of moving coil galvanomete eflection is popotional to the cuent passing though the galvanomete. ( ) G S So, G CS = = G G CS G (A) G G () An as in case of a shunte galvanomete with S = (G/n) ( G ) n G = G G i.e., G = ( n) So, CS = CS ( n) E.. Two long paallel wies caying cuents.5 A an A iecte into the plane of the pape ae hel at P an Q espectively such that these ae pepenicula to the plane of the pape. The points P an Q ae locate at a istance of 5 metes an metes espectively fom a collinea point as shown in the figue. (i) An electon moving with a velocity of 4 5 m/s along the positive - iection epeiences a foce of magnitue. N at the point. Fin the value of Y P Q.5A m 5m X (ii) Fin all the positions at which a thi long paallel wie caying a cuent of magnitue.5 A must be place so that the magnetic inuction at is zeo. Sol.: (i) The magnetic fiel inuction at point ue to cuent in wies P an Q = = + whee = = along negative Y-ais (magnetic fiel ue to P) along negative Y-ais (magnetic fiel ue to Q) = along negative Y-ais. o.5 = 7 5 j = 7 [ + ] j

19 As F = qv = (.6 9 ) [(4 5 )i { 7 ( +) j}] = 6.4 ( +)k F = 6.4 ( +) =. N o + = 5, = 4A. (ii) The thi wie can be place on eithe sie of to pouce a fiel (by passing cuent in opposite iections) which will neutalise the magnetic fiels of the fist two cuents, then = + + = = ± m fom along X-ais. E.. Fin the magnetic inuction at point if the wies caying a cuent has shapes as shown in Figues, an. The linea pats of the wies ae vey long an the cuve pat is a semicicula one with aius. Z Y Z Y Z Y X X Sol.: The magnetic fiel ue to linea pat = 4 X The magnetic fiel ue to semicicula pat = 4 The magnetic inuction at point = = + + = ( k) ( i) ( k) = i k Magnitue of magnetic inuction = = Magnetic inuction at = = + + = ( k) ( i) ( i) = ( ) i k 4 ( ) 4 =

20 Magnetic inuction at = = + + = ( k) ( i) ( j) = i j k 4 = () () = E.. Two paallel hoizontal conuctos ae suspene each by light vetical theas.75 m long. Each conucto has a mass of 4 gm pe mete. These conuctos ae sepaate by 5 mm when thee is no cuent flowing in the wies. f equal amount of cuent is passe though each of the wies, these conuctos ae sepaate by.5 cm. Fin the value an iection of the cuent. Sol. n oe that these conuctos ae epelle, the cuents shoul flow in opposite iections in these wies. Let each vetical theas be eflecte though an equal angle ue to symmety. The foce of epulsion epeience pe unit length of eithe conucto (F) is given by F = F = magnetic fiel ue to one conucto on the othe cuent flowing though the othe conucto. Whee the cuent though each conucto is an is sepaation between them. Each conucto has this foce F, tension T in the thea an weight acting as shown in the iagam. Fo equilibium, T cos = mg, T sin = F, whee m is the mass pe unit length of the conucto. F tan = = = mg 4 mg As angle is small, tan sin = 4 mg sin = = mg.5.75 m g sin 7 T F mg.75m.5cm.5cm T mg F = = = 96 = 4 ampee E.. A small hoizontal wie A, which is fee to move in a vetical plane an caies a cuent of A, is in equilibium at a height of. m ove anothe paallel long wie CD, which is fie in a hoizontal plane an caies a steay cuent of A. Show that when A is slightly epesse an elease, it eecutes S.H.M. Fin the peio of oscillations.

21 Sol. The magnetic foce on A is upwas an is epulsive in natue. f an ae cuents between two wies sepaate by istance h, the foce F pe unit length, F = A F A ^ h C h mg D n equilibium, the weight mg of uppe wie is balance by the magnetic foce F. A h = mg (whee m is mass of unit length of o A) Let the wie A be epesse vetically ownwas though a istance y, the epulsion will incease as h y < h an the wie will ten to go back to its oiginal position when it is elease. The net foce F' is, theefoe, given by F' = mg h y = mg h mg h y mgy h y o estoing foce F' = mgy ( h y) Fo small isplacements, y <<h, F' = mg h y ky As F' is popotional to isplacement y an is opposite to it, the uppe wie will eecute S.H.M. with foce constant k = mg/h. Time peio of oscillation = T = π m k π h g π =. secon.. E.4. Thee infinitely long thin wies, each caying cuent in the same iection, ae in the y plane of a gavity fee space. The cental wie is along the y-ais while the othe two ae along = + an =, (i) (ii) Fin the locus fo points fo which the magnetic fiel is zeo. f the cental wie is isplace along the z iection by a small amount an elease, show that it will eecute simple hamonic motion. f the linea ensity of wie is, fin the fequency of oscillation. Sol. (i) Consie thee wies A, an C each caying a cuent. Let P be point at a istant fom whee the esultant magnetic fiel P is zeo.

22 P = ) ( ) ( k P C A y + o = o =, The locus of points fo which the magnetic fiel is zeo ae the lines = an =. (ii) When the cental wie is isplace along the z iection, the foces on it ue to othe two wies will be F' each an the esultant foce F = F' sin whee A C F = z z l F F C A z z = z l z z l ~ ) ( ( z << ) This foce is iectly popotional to the isplacement z an is iecte towas the mean position. The cental wie will eecute S.H.M. Foce constant k = l mass of length of the wie = m = l, whee l is length of wie. Fequency of oscillation, f = m k = l l f = E.5. A non-conucting sphee of aius = 5 mm chage unifomly with suface ensity =. µc/m² otates with an angula velocity = 7 a/s about the ais passing though its cente. Fin the magnetic inuction at the cente of the sphee. Sol. The sphee is non-conucting an hence the chage will be on the oute suface. A otating chage sphee will behave like a pile of cuent loops of vaying aii. Consie a ing as shown in figue.

23 Aea of the angula ing = ( sin ) an aea of this cuent loop = ( sin ) The equivalent cuent ue to ing element i = chage time aea suface chage time ensity Magnetic inuction at the cente ue to the ing = sin ( / ) = ² sin A = i Aea of the cuen loop i = ( sin ) = sin i = = sin sin sin sin = sin = E.6. A iect cuent flowing though the wining of a long cylinical solenoi of aius pouces in it a unifom magnetic fiel of inuction. An electon falls into the solenoi along the aius between its tun (at ight angles to the solenoi ais) at a velocity. v. Afte a cetain time the electon is eflecte by magnetic fiel an leaves the solenoi. Calculate the time uing which the electon moves in the solenoi. Sol. The magnetic inuction of the solenoi is iecte along its ais. So, the Loentz foce (F = ev ) on the electon at any time will be in a plane pepenicula to solenoi ais. The tajectoy of the electon in the solenoi will be an ac of the cicle. The aius given by ev = mv o mv e... (i) The tajectoy of the electon is shown in the figue. n the figue, A an C ae tangents to the electon tajectoy at points A an C. Let AC be Fom figue A = / AC tan...(ii)

24 Fom equations (i) an (ii) e = tan mv...(iii) The magnitue of velocity emains unchange ove the entie tajectoy because the Loentz foce is pepenicula to the velocity at any instant. Thus the tansit time t given by t = v m e = m e tan e mv E.7. A pai of paallel hoizontal conucting ails of negligible esistance shote at one en is fie on a table. The istance between the ails is L. A conucting massless o of esistance can slie on the ails fictionlessly. The o is tie to a massless sting which passes ove a pullely fie to the ege of the table. A mass m, tie to the othe en of sting, hangs vetically. A constant magnetic fiel eists pepenicula to the table. f the system is elease fom est, calculate. L the teminal velocity achieve by the o the acceleation of the mass at the instant when the velocity of o is half the teminal velocity. Sol. When teminal velocity is achieve T = i L = mg (whee i is inuce cuent) nuce emf e = Lv T sin 9 = Lv T L v T i = whee v T is teminal velocity. L v T T mg mg v... (i) L Let the block have velocity v at any time t befoe it achieves the teminal velocity. Acceleation of block. mg T a m mg ( L v / ) m mg il (T = il because o is massless) m il T T mg

25 When v v T, then mg a L ( v m T / ) L ( mg / L g m ) g g g E.8. A small chage ball having mass m an chage q is suspene fom a igi suppot by means of an inetensible thea of length l. t is mae to otate on a hoizontal cicula path in a unifom time inepenent magnetic fiel of inuction which is iecte upwa. The time peio of evolution of the ball is T. f the thea is always stetche, calculate the aius of cicula path on which the ball moves. Sol. The moving chage epeiences a foce in the magnetic fiel. This foce povies the centipetal foce that keeps the ball in a cicula obit. The foce acting on the ball ae shown in the figue. Fo cicula hoizntal path, T cos = mg... (i) Y P an T sin q v = (mv²/) Fom equation (ii)...(ii) l T l mg cos sin q = m ² [ v = an T = mg/cos fom (i)] T cos q v q mg T sin Fom figue, sin an cos t (l ) l ( l mg ) q q = m ² o ( l ) g mg (/ ) o (l² ²) = [( / g) ( q / mg)] (T' / ) o (l² ²) = [( / g T' ) ( q / mg)] l (T' / ) {(/ g T' ) q( / mg)}

26 E.9. A unifom; constant magnetic fiel is iecte at an angle of 45 to the ais in y plane. PQS is a igi squae wie fame caying a steay cuent, with its cente at the oigin. At time t =, the fame is at est in the position shown in the figue, with its sie paallel to an y aes. Each sie of the fame is of mass M an length L. (i) What is the toque about acting on the fame ue to magnetic fiel? S P Y X Q (ii) Fin the angle by which the fame otates une the action of this toque in a shot inteval of time t, an the ais about which this otation occus. (t is so shot that any vaiation in the toque uing this inteval may be neglecte). Given: the moment of inetia of the fame about an ais though its cente pepenicula to its plane 4 is m L. Sol. (i) = (cos 45 i +sin 45 j) an A = L² k (ii) Now = M whee M = A = [L² k (cos 45 i + sin 45 j)] = L² [cos 45 j + sin 45 ( i)] = L ( i + j) Ais of otation is along unit vecto ( i j) S Q in its plane an magnitue of toque = L² i.e., the fame will epeience a toque about ais Applying the theoem of pepenicula aes, the moment of inetia about the ais of otation S Q = = 4 ML Angula acceleation = τ ML o L ( i j) ( i j), α / ML M M Using = t + t fo small t, can be assume to be constant = t² = (t)² M 4M

27 JECTVE QUESTNS. Two cicula coils P an Q ae mae fom simila wies but aius of Q is twice that of P. What shoul be the value of potential iffeence acoss them so that the magnetic inuction at thei cente may be the same? V q = V p V q = V P V q = 4V p V q = /4 V p. The aius of the cicula path o helical path followe by the test change q moving in magnetic fiel with velocity v is m v sin q m v cos q m v q m v tan q. An electon acceleate though a potential iffeence V entes into a unifom tansvese magnetic fiel an epeiences a foce F. f the acceleating potential is incease to V, the electon in the same magnetic fiel will epeience a foce : F F/ F F 4. A chage paticle moving in a unifom magnetic fiel penetates a laye of lea an loses one half of its kinetic enegy. The atio of aius of cuvatue to the oiginal aius is 5. Two staight long conuctos A an CD ae pepenicula to each othe an cay cuents i an i. The magnitue of the magnetic inuction at a point P at a istance fom the point in a iection pepenicula to the plane ACD is ( i i) ( i i) 4 / ( i i ) ii i i 6. A cuent of amp. is flowing in a wie of length.5 mete. A foce of 5 newton acts on it when it is place in a unifom magnetic fiel of tesla. The angle between the magnetic fiel an the iection of cuent is º 45º 6º 9º 7. A paticle caying a chage equal to times the chage on an electon is otating pe secon in a cicula path of aius.8 m. The value of the magnetic fiel pouce at the cente will be ( = pemeability constant). 7 / 7 6 / C 7 8. The magnetic fiel at the cente of the cicula potion of the cuent caying wie of aius cm is (8/) 5 T (8/) 4 T 5 T 4 T 4Amp. A / D E

28 9. A long wie caies a cuent of A along the ais of a solenoi. The fiel ue to the solenoi is 4 mt. the esultant fiel at a point mm fom the solenoi ais is. m T 4. mt. m T 8.4 m T. A cicula cuent caying coil has a aius. The istance fom the cente of the coil on the ais whee the magnetic inuction will be (/8)th of its value at the cente of the coil is / /. A poton moving with a constant velocity passes though a egion of space without any change in its velocity. f E an epesent the electic an magnetic fiels espectively, ientify wong statement E =, = E =, E, = E,. An electon is moving in a cicle of aius in a unifom magnetic fiel. Suenly the fiel is euce to /. The aius of the cicle now becomes / /4 4. A poton an an -paticle, moving with the same kinetic enegy, entes a unifom magnetic fiel nomally. The aii of thei cicula paths will be in the atio : : : 4 : 4. A beam of electons is acceleate though a potential iffeence V. t is then passe nomally though a unifom magnetic fiel whee it moves in a cicle of aius. t woul have move in a cicle of aius if it wee initially acceleate though a potential iffeence V V V 4V 5. A poton an an -paticle, acceleate though the same potential iffeence, ente a egion of unifom magnetic fiel nomally. f the aius of the poton obit is cm then the aius of of the -obit is cm cm cm 5 cm 6. Two paticles X an Y having equal chage, afte being acceleate though the same potential iffeence, ente a egion of unifom magnetic fiel an escibe cicula paths of aii an espectively. The atio of the mass of X to that of Y is ( / ) / / ( / ) / 7. A paticle of chage +q an mass m moving une the influence of a unifom electic fiel Ei an a unifom magnetic fiel k follows a tajectoy fom P to Q as shown in the figue. The velocities at P an Q ae v i an v j. Which of the following statements is incoect E 4 m v qa y P v E ate of wok one by the electic fiel at P is m v 4 a ate of wok one by the electic fiel at P is zeo ate of wok one by both the fiels at Q is zeo a Q v

29 8. A hoizontal wie of length cm an mass. g caies a cuent of 5 A. The magnitue of the magnetic fiel which can suppot the weight of the wie is (g = m/s ) T 6 T 4 T 6 4 T 9. A MeV poton (mass =.6 7 kg) is moving pepenicula to a unifom magnetic fiel of.5 T. The magnetic foce on the poton is.5 N 8 N.5 N 8 N. A potion of a long staight wie, caying a cuent, is bent in the fom of a semicicle of aius as shown in the figue. The magnetic fiel at the cente of the semicicle, in tesla, is 7 7. A long staight conucto, caying a cuent, is bent into the shape shown in the figue. The aius of the cicula loop is. The magnetic fiel at the cente of the loop is into the page out of the page into the page out of the page. A ectangula loop caying a cuent i is situate nea a long staight wie such that the wie is paallel to one of the sies of the loop an is in the plane of the loop. f a steay cuent is establishe in the wie as shown in the figue, the loop will otate about an ais paallel to the wie move away fom the wie move towas the wie emain stationay i. A squae coil of sie a caies a cuent. The magnetic fiel at the cente of the coil is a a a a a 4. A cicula cuent -caying coil has a aius. The istance fom the cente of the coil, on the ais, whee will be /8th of its value at the cente of the coil is /

30 5. n a figue A is a long staight wie caying a cuent of A an CDFG is a ectangula loop of size cm 9 cm caying a cuent of A. The ege CG is paallel to A, at a istance of cm fom it. The foce eete on the loop by the magnetic fiel of the wie is C D cm 9cm A A cm A G F.6 4 N towas left.6 4 N towas ight 7. 4 N towas ight 7. 4 N towas left 6. n the figue, y an z ae long staight wies. The magnetic foce on 5 cm length of y is 4 N towas ight 4 4 N towas ight 4 N towas left 4 4 N towas left y z A A A cm cm 7. A cuent of ampee flows in a wie foming a cicula ac of aius metes subtening an angle at the cente as shown. The magnetic fiel at the cente in tesla is n the given loop, the magnetic fiel at the cente is 4 out of the page 4 into the page 4 out of the page out of the page

31 9. A poton an an -paticle ente a unifom magnetic fiel pepeniculaly, with the same spee. f the poton takes 5 micosecons to make 5 evolutions, the peioic time fo the -paticle woul be 5 s 5 s s 5 s. A poton, a euteon an an -paticle, having the same kinetic enegy, ae moving in cicula tajectoies in a constant magnetic fiel. f p, an enote, espectively, the aii of the tajectoies of these paticles, then = p < > > p = > p p = < ME THAN NE CECT CHCE. Velocity an acceleation vecto of a chage paticle moving in a magnetic fiel at some instant ae v iˆ 4j ˆ an a i ˆ j ˆ. Select the coect altenatives =.5 = magnetic fiel is along z-iection Q kinetic enegy of the paticle is constant. A nonconucting isc having unifom positive chage Q, is otating about its vetical ais passing though its cente of mass with unifom angula velocity. The magnetic fiel at the cente of the isc is iecte hoizontally having magnitue iecte vetically. Magnitue of magnetic fiel at the cente ue to wie is zeo wie an wie is zeo wie 4 is zeo wie an wie = wie an wie 4 having magnitue 4. A paticle of chage +q an mass m moving une the influence of a unifom electic fiel ˆ Ei an a unifom magnetic fiel Q ae ˆ vi an mv E 4 qa Q 4 Q ˆ k follows a tajectoy fom P to Q as shown in figue. The velocities at P an v. Which of the following statement(s) is/ae coect? mv ate of wok one by the electic fiel at P is 4 a ate of wok one by the electic fiel at P is zeo ate of wok one by both the fiels at Q is zeo. P a y a E v Q v

32 5 A steay cuent is set up in a netwok compose of wies of equal esistances as shown in fig.a an. What is the magneitc fiel at the cente P in each case? C A P C A D P E F D H G ( ) ( ) (A) () it is Zeo in case (A) it is Zeo in case () it is not Zeo in case (A) it is not Zeo in case () 6. A chage paticle is pojecte in a plane pepenicula to unifom magnetic fiel. The aeal velocity (aea swept pe unit time) of the paticle is iectly popotional to kinetic enegy of paticle iectly popotional to momentum of the paticle invesely popotional to magnetic fiel stength invesely popotional to chage on paticle 7. A poton moving with a constant velocity passes though egion of space without any change in its velocity. f E an epesent the electic an magnetic fiels espectively, this egion of space may have E =, = E =, E, = E, 8. Two long conucting wies caying equal cuents ae place paallel to the z-ais. A chage paticle is mae to move in a cicula path of aius a with cente of the path at point (, a) in clockwise iection. Duing the couse of motion, it passes though fou points P, Q, an S having cooinates (, a), ( a, a), (, a) an (a, a) espectively. The magnitue of foce eete on the paticle by the magnetic fiel ceate by the wies is maimum when it passes though point y (,a) ( a, ) (a, ) P Q SD

33 9. A pactice of chage q an mass m entes nomally (at point P) in a egion of magnetic fiel with spee v. t comes out nomally fom Q afte time T as shown in figue. The magnetic fiel is pesent only in the egion of aius an is unifom. nitial an final velocities ae along aial iection an they ae pepenicula to each othe. Fo this to happen, which of the following epession(s) is/ae coect v P Q v mv q T v m T q None of these 4. A battey is connecte between two points A an on the cicumfeence of a unifom conucting ing of aius an esistance as shown in figue. ne of the ac A of the ing subtens an angle at the cente. What is the value of the magnetic fiel at the cente ue to the cuent in the ing? it is Zeo always it is non zeo always magnetic fiel epens on magnetic fiel oes not epen on

34 MSCELLANEUS ASSGNMENT Compehension- Magnetic fiel intensity () ue to cuent caying conucto can be calculate by use of iot-savat l law. which is =, whee is magnetic fiel ue cuent element l at a position 4 fom cuent element. Fo staight wie caying cuent magneticfiel at a istance fom wie is = (sin + sin ) an magnetic fiel ue to a cicula ac at its cente is = 4 angle of cicula ac at cente, is aius of cicula ac.. whee 4 P Now answe the following questions.. The magnetic fiel at C ue to cuve pat is, iecte into the plane of the pape 6a, iecte towas you a, iecte towas you 6a, iecte up the plane of the pape a. A wie loop caying a cuent is shown in figue. The magnetic fiel inuction at C ue to staight pat is, iecte up the plane of the pape a, iecte into the plane of the pape 6a, iecte towas you 6a a a C a towas you. The net magnetic fiel at C ue to the cuent caying loop is zeo a 9a a, iecte into the plane of the pape

35 Compehension- A cuent caying coil behave like shot magnet whose magnetic ipole moment M = n A. Whee iection of M is taken along the iection of magnetic fiel on its ais an n is no of tums A is aea of coil an is cuent flowing though coil. When such a coil is put in magnetic fiel () magnetic toque () acts ove it as = M an potential enegy in of the cuent loop in the magnetic fiel is u = M. 4. A cuent of A is flowing in a plane cicula coil of aius 4 cm an having tuns. The coil is place in a unifom magnetic fiel of.5 Wb m. Then, the ipole moment of the coil is A m. A m 75 A m.88 A m 5. A cuent of A is flowing in a plane cicula coil of aius 4 cm an having tuns. The coil is place in a unifom magnetic fiel of.5 Wb m. Then, the P.E. of the magnetic ipole in the position of stable equilibium is 5 J 9.4 mj +.5 J +5 J 6. n above question, to hol the cuent-caying coil with nomal to its plane making an angle of 9 with the iection of magnetic inuction, the necessay toque is 5 Nm 9.4 Nm 5 Nm 5 Nm 7. Column gives foce epession fo cuent caying wie shown in column match them coectly. Column Column A. (p) i. (q) zeo C. () i D. (s) i

36 8. Column gives value of magnetic fiel ue to coaial cable consists of an inne wie of aius a suoune by an oute shell of inne an oute aii b an c espectively. The inne wie caies an cuent i an oute shell caies an equal cuent in opposite iection, at a istance fom ais fo position given in column match them coectly Column A. < a (p). a < < b (q) zeo Column i (c ) (c b ) C. b < < c () D. > c (s) i a i 9. A paticle moves in a cicula path of iamete. m une the action of magnetic fiel of.4 Tesla. An electic fiel of V/m makes the path of paticle staight. The chage / mass atio of the paticle is.5 n 5 C/kg. Fin the value of n.. A m long conucting wie is lying at ight angles to the magnetic fiel. A foce of kg. wt is acting on it in a magnetic fiel of.98 Tesla. The cuent flowing in it is 5n Ampee. Fin the value of n.. A cuent is flowing in a cicula conucto of aius. t is lying in a unifom magnetic fiel such that its plane is nomal to it. What will be magnetic foce acting on the loop.. A cycloton in which the magnetic flu ensity is.4 tesla is use to acceleate potons. With. n 7 Hz fequency the electic fiel between the "ees" is evese. Fin the value of n. Given : mass of poton =.67 7 kg.. A unifom magnetic fiel of.5 T eists in a cylinical egion of aius. cm, its iection paallel to the ais along east to west. A wie caying cuent of 7. A in the noth to south iection passes though this egion. of.7 n Newton foce on the wie woks if, the wie intesects the ais. Fin the value of n. 4. A.5 kg coppe o ests on two hoizontal ails 95. cm apat an caies a cuent of 5. A fom one ail to the othe. The coefficient of static fiction is.58. The smallest magnetic fiel (not necessay vetical) is. n T that woul cause the ba to slie. Fin the value of n. 5. Two cicula coils ae mae of two ientical wies of same length. f the numbe of tuns of the two coils ae 4 an. Fin out the atio of magnetic inuction at centes of them. 6. A poton moves in a cicula path pepenicula to a magnetic fiel. f the intensity of the magnetic fiel is ouble but the aius of the cicula path is constant, then fin how many times the kinetic enegy of the paticle will be?

37 7. A. cm wie caying a cuent of A is place insie a solenoi pepenicula to its ais. The magnetic fiel insie the solenoi is given to be.7 T. The magnetic foce on the wie is.9 n N. Fin the value of n. 8. The fequency of oscillating potential applie to the ees of a cycloton is 8 6 Hz. The magnetic fiel equie to acceleate an -paticle is. n T. Fin the value of n. Given : mass of -paticle = kg.

38 PEVUS YEA QUESTNS T-JEE/JEE-ADVANCE QUESTNS. A cuent flows along the length of an infinitely long, staight, thin walle pipe. Then the magnetic fiel at all points insie the pipe is the same, but not zeo the magnetic fiel at any point insie the pipe is zeo the magnetic fiel is zeo only on the ais of the pipe the magnetic fiel is iffeent at iffeent points insie the pipe.. An electon of mass m e, initially at est, moves though a cetain istance in a unifom electic fiel in time t. A poton of mass m p, also, initially at est, takes time t to move though an equal istance in this unifom electic fiel. Neglecting the effect of gavity, the atio of t /t is nealy equal to (m p /m e ) / (m e /m p ) / 86. A poton, a euteon an an paticle having the same kinetic enegy ae moving in cicula tajectoies in a constant magnetic fiel. f p, an enote espectively aii of the tajectoies of these paticles, then = p < > > p = > p p = = 4. A chage paticle is elease fom est in a egion of steay an unifom electic an magnetic fiels which ae paallel to each othe. The paticle will move in a staight line cicle heli cycloi 5. Two long paallel wies ae at a istance apat. They cay steay an equal cuents flowing out of the plane of the pape as shown. The vaiation of the magnetic fiel along the line XX is given by 6. A non-plana loop of conucting wie caying a cuent is place as shown in the figue. Each of the staight section of the loop is of length a. The magnetic fiel ue to this loop at the point P(a,, a) points in the iection ( ˆ ˆ j k) ( iˆ ˆj kˆ ) (ˆ ˆ ˆ i j k) (ˆ i kˆ )

39 7. A paticle of mass m an chage q moves with a constant velocity v along the positive iection. t entes a egion containing a unifom magnetic fiel iecte along the negative z-iection etening fom = a to = b. The minimum value of v equie so that the paticle can just ente the egion > b is qb/m q(b a)/m qa/m q(b + a)/m 8. A long staight wie of cicula coss-section is mae of a non-magnetic mateial. The wie is of aius a. The wie caies a cuent which is unifomly istibute ove its coss-section. The enegy stoe pe unit length in the magnetic fiel containe within the wie is U = 8 U= 6 U = 4 U = 9. A ba magnet is falling towas a fie close conucting loop of aius. At t = s, the possible istance move by the magnet towas the loop in mete is 8. An infinite cuent caying wie passes though point an is pepenicula to the plane containing a cuent caying loop ACD as shown in the figue. Choose the coect option (s). Net foce on the loop is zeo Net toque on the loop is zeo As seen fom, the loop otates clockwise As seen fom, the loop otates anticlockwise. A magnetic fiel ˆ j eists in the egion a < < a an ˆ j, in the egion a < < a, whee is a positive constant. A positive point chage moving with a velocity v v ˆ i, whee v is a positive constant, entes the magnetic fiel at = a. The tajectoy of the chage in this egion can [T 7 ] A C D (q)

40 . Statement-: A vetical ion o has a coil of wie woun ove it at the bottom because Statement-: en. An altenating cuent flows in the coil. The o goes though a conucting ing as shown in the figue. The ing can float at a cetain height above the coil. n the above situation, a cuent is inuce in the ing which inteacts with the hoizontal component of the magnetic fiel to pouce an aveage foce in the upwa iection. Statement- is Tue, Statement- is Tue; Statement- is a coect eplanation fo Statement- Statement- an is Tue; Statement- is NT a coect eplanation fo Statement- Statement- is Tue, Statement- is False Statement- is False, Statement- is Tue. A paticle of mass m an chage q, moving with velocity V entes egion nomal to the bounay as shown in the figue. egion has a unifom magnetic fiel pepenicula to the plane of the pape. The length of the egion is l. Choose the coect choice(s). egion egion egion The paticle entes egion only if its velocity ql V m V ql The paticle entes egion only if its velocity V m l ql Path length of the paticle in egion is maimum when velocity V m Time spent in egion is same fo any velocity V as long as the paticle etuns to egion 4. STATEMENT-: The sensitivity of a moving coil galvanomete is incease by placing a suitable magnetic mateial as a coe insie the coil. STATEMENT-: Soft ion has a high magnetic pemeability an cannot be easily magnetize o emagnetize. Statement- is Tue, Statement- is Tue; Statement- is a coect eplanation fo Statement- Statement- an is Tue; Statement- is NT a coect eplanation fo Statement- Statement- is Tue, Statement- is False 5. The figue shows cetain wie segments joine togethe to fom a coplana loop. The loop is place in a pepenicula magnetic fiel in the iection going into the plane of the figue. The magnitue of the fiel inceases with time. an ae the cuents in the segments ab an c. Then, c > < is in the iection ba an is in the iection c is in the iection ab an is in the iection c a b