MAGNETIC EFFECT OF CURRENT AND MAGNETISM

Transcription

1 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC MAGNETIC EFFECT OF CURRENT AND MAGNETISM Syllabus : Biot - Savat law and its application of cuent caying cicula loop. Ampee s law and its application to infinitely long cuent caying staight wie and solenoid. Foce on a moving chage in unifom magnetic and electic fields, Cycloton, Foce on a cuent-caying conducto in a unifom magnetic field. Foce between two paallel cuent-caying conductos-definition of ampee. Toque expeienced by a cuent loop in unifom magnetic field; Moving coil galvanomete, its cuent sensitivity and convesion to ammete and voltmete. Cuent loop as a magnetic dipole and its magnetic dipole moment. Ba magnet as an equivalent solenoid, magnetic field lines; Eath s magnetic field and magnetic elements. Paa-, dia- and feo-magnetic substances. Magnetic susceptibility and pemeability, Hysteesis, Electomagnets and pemanent magnets.

2 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC C O N C E P T S C SOURCE OF MAGNETIC FIELD CA Magnetic field of unifomly moving chage : A moving electic chage ceates a magnetic field in the space aound it. The law defining the magnetic field B of a point chage moving at a constant non-elativistic velocity v (v ) is witten as B q 4 3 whee is the magnetic constant, the coefficient 7 4 H / m, and is the adius vecto fom the C C3 point chage q to the point whee the field is to be detemined as shown in figue. The diection of B can be obtained by applying scew ule on v. MAGNETIC FIELD OF A CURRENT ELEMENT The law of Biot and Savat gives the magnetic field ceated by a small elements of length dl caying a dl cuent I. Accoding to this law : db I whee d l vecto points in the diection of cuent 4 3 I. The vecto goes fom the cuent element to the point whee the field db can be obtained by applying the scew ule (d l ). This law can be used to find the magnetic field ceated by any configuation of cuent caying wie. MAGNETIC FIELD FOR SOME IMPORTANT CONFIGURATION. A staight cuent caying wie case a : case b : Conside a wie AB caying cuent I as shown in figue. Fo points along the length of the wie the field is always zeo. I The magnetic field at point P is given by B (cos cos) 4 case c : case d : If the wie is of infinite length then the field at P is I. 4 B case e : The magnetic field at point P is given by Icos B 4 If the wie is of semi infinite length then the field at P is given by I. 4 B

3 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 3. A cicula cuent loop Conside a cuent loop of adius caying a cuent I and having N tuns. Field at cente of the loop : NI B 4 Field at axis passing though the cente and pependicula to the plane of the loop : Note that only axial component of the field will exist. 3. A Cuent Ac I Il Field at cente of the ac is B, 4 4 whee l is the length of the ac and is the angle made by the ac at the cente. 4. Solenoid NI B 4 ( x ) 3/ If seveal tuns of an insulated wies ae wounded aound the cylinde then the esulting coil is called a solenoid. Field at an axial point of a solenoid is given by B (ni)[cos cos] 4 Hee n is then numbe of tuns pe unit length. case a : If the solenoid is of infinite length then B = ni case b : Field nea the end of an infinite solenoid is case c : Field outside the solenoid is zeo. ni. Conventionally the diection of the field pependicula to the plane of the pape is epesented by if into the page and if out of the page. Pactice Poblems :. A squae coil of side a caies a cuent I. The magnetic field at the cente of the coil is I a I a I a I a. Two cicula coils have numbe of tuns in the atio : and adii in the atio :. If the same cuent flows though them, the magnetic fields at thei centes will be in the atio : : : : 4 3. The magnetic field inside a cuent caying tooidal solenoid is B. If its adius is doubled and the cuent though it is also doubled, the magnetic field inside the solenoid will be B/ B B 4B

4 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 4 4. Two identical coils have a common cente and thei planes ae at ight angles to each othe. They cay equal cuents. If the magnitude of the magnetic field at the cente due to one of the coils is B then that due to the combination is B B B/ B 5. A cuent of A is flowing in the sides of an equilateal tiangle of side 4.5 m. The magnetic field at the centoid of the tiangle is 5 T 4 5 T 8 5 T. 4 T 6. Match the following column : Column-I Column-II (p) (i) I I out of the page 4 4 I (q) (ii) 4 out of the page () (iii) I 4 into the page (p)-(i), (q)-(ii), ()-(iii) (p)-(ii), (q)-(i), ()-(iii) (p)-(iii), (q)-(ii), ()-(i) (p)-(i), (q)-(iii), ()-(ii) [Answes : () d () d (3) c (4) b (5) b (6) a] C4A MAGNETIC FORCE ON MOVING CHARGES A magnetic field exets a foce on a moving chage but not on a stationay chaged paticle. The foce on a chage q moving with velocity v in a magnetic field B is given by F q(v B). F = q v B sin whee is the angle between the B and velocity v. The diection of F is given by ight hand scew ule. The foce on a positive chage is in the diection of v B but the foce on a negative chage is opposite to the vecto v B. Fo v B, F = and fo F qvb C4B Note that foce F is always pependicula to v, so it cannot change the magnitude of velocity, only its diection. So the magnetic field can neve do wok on the paticle and this is tue even if the magnetic field is not unifom. Hence the kinetic enegy of the paticle is constant. MOTION OF CHARGED PARTICLE IN A MAGNETIC FIELD Case I Motion in Staight Line A chaged paticle pojected into a magnetic field with a velocity paallel o antipaallel to the field, expeiences a zeo foce. Hence the velocity of this paticle in this case is constant and hence it tavels in a staight line. Case II Motion on a Cicula Path A chaged paticle of chage q, pojected into a magnetic field B with initial velocity v pependicula to the field, expeiences a foce F = qvb. Unde the action of such foce the paticle moves in a cicula path with constant speed. The plane of the cicula path is pependicula to the lines of foce of the magnetic field.

5 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 The magnetic foce povides the centipetal foce. Accoding to Newton s Second Law qvb mv mv qb PMEC 5 whee is the adius of the cicula path. T gives the time peiod of evolution which is given by m v qb Note that time peiod is independent of velocity. Case III Helical Motion. Conside a positive chaged q has velocity components both pependicula ( v ) and paallel (v ) to a magnetic field B then it moves in a path, shown in figue, called helical path. The (v ) and ( v ) component is esponsible fo linea motion and cicula motion espectively of the paticle and hence the esulting motion is helical. Radius of helix, mv qb. Time peiod of evolution, T m qb. p v m qb T v Pitch of the helix (the displacement paallel to the field in one evolution) is Pactice Poblems :. A chaged paticle entes a magnetic field such that the diection of initial velocity is diffeent fom the diection of the field. Which of the following chaacteistics of the paticle doesn t change with time? momentum kinetic enegy acceleation diection of motion. Choose the coect statement fo the magnetic foce acting on a chaged paticle The maximum mgnetic foce will be when the velocity of the chaged paticle is pependicula to the diection of magnetic field. Powe acted by the magnetic foce is always zeo Wok done by the magnetic foce is always zeo All ae coect 3. Ions of diffeent momenta (p), having the same chage, ente nomally a unifom magnetic field. The adius of the obit of an ion is popotional to p /p p /p 4. A poton and an -paticle, moving with the same kinetic enegy, ente a unifom magnetic field nomally. The adii of thei cicula paths will be in the atio : : : 4 : 5. Two paticles X and Y having chage, afte being acceleated though the same potential diffeence ente a egion of unifom magnetic field and descibe cicula paths of adii R and R espectively. The atio of the mass of X to that of Y is (R / R ) / R /R (R / R ) R /R 6. An electon is injected into a unifom magnetic field with components of velocity paallel to and nomal to the field diection. The path of the electon is a helix cicle paabola staight line 7. A poton and an -paticle ente a unifom magnetic field pependiculaly, with the same speed. If the poton takes 5 micoseconds to make 5 evolutions, the peiodic time fo the -paticle would be 5 s 5 s s 5 s

6 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 6 8. If a paticle of chage C moving along the x-diection with a velocity 5 m/s expeiences a foce of N in y-diection, then the minimum magnetic field is T in the positive z-diection 5 T in the negative z-diection 3 T in the positive z-diection 3 T in the negative z-diection [Answes : () b () d (3) a (4) a (5) c (6) a (7) c (8) d] C5 LORENTZ FORCE When a chaged paticle moves though a egion of space whee both electic and magnetic field ae pesent, both fields exets foces on the paticle. The total foce F is the vecto sum of the electic and magnetic foce on a chaged paticle of chage q is given by F q(e v B), this foce is known as Loentz foce. Pactice Poblems :. A unifom electic field and a unifom magnetic field exist in a egion in the same diection. An electon is pojected with velocity pointed in the same diection. The electon will follow a staight path cicula path Helix path Cycloidal path. A poton moving with a constant velocity passes though a egion of space without any change in its velocity. If E and B epesent the electic and magnetic fields espectively, this egion of space may not have E =, B = E =, B E, B = E, B 3. A chaged paticle entes a egion whee a unifom electic field E and a unifom magnetic field B exist. If E and B ae pependicula to each othe and also pependicula to the velocity u of the paticle, then the paticle will move undeviated if u equals B/E E/B EB E /B [Answes : () a () c (3) b] C6A FORCE ON A CURRENT CARRYING CONDUCTOR The foce expeienced by cuent element of length dl caying cuent I placed in a magnetic field B is given by F I(dl B. df Idl B. The total foce on a cuent caying conducto is given by ) If the field B is unifom and cuent I is steady, then F I ( dl ) B Il B C6B whee l is the vecto whose magnitude is l and the diection is same as that of cuent. Hence the foce on a wie of abitay shape is same as that on a staight wie joining the end points of the wie of abitay shape. Fom the above statement we can conclude that the foce acting on a closed loop caying steady state cuent placed in a unifom field is zeo. FORCE BETWEEN TWO PARALLEL CURRENT CARRYING WIRES Conside two long wies kept paallel to each othe, distance d apat, and caying cuents I and I espectively, then (i) (ii) if they cay cuents in the same diection then thee will be foce of attaction between them. if they cay cuent in the opposite diection then thee will foce of epulsion between them. The magnitude of foce expeienced by each wie on a unit length is given as foce pe unit II length =. 4 d

7 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 Pactice Poblems : PMEC 7. A hoizontal wie of length cm and mass.3 g caies a cuent of 5A. The magnitude of the magnetic field which can suppot the weight of the wie is (g = m/s ). 3 3 T 6 3 T 3 4 T 6 4 T. A vetical wie caying a cuent in the upwad diection is placed in a hoizontal magnetic field diected towads noth. The wie will expeience a foce towads Noth South East West 3. A long hoizontally fixed wie caies a cuent of A. Diectly above and paallel to it is anothe wie caying a cuent of A and weighing.4 N/m. What should be the sepaation between the two wies so that the uppe wie is just suppoted by magnetic epulsion? cm cm 3 cm 4 cm 4. In the figue AB is a long staight wie caying a cuent of A and CDFG is a ectangula loop of size cm 9 cm caying a cuent of A. The edge CG is paallel to AB, at a distance of cm fom it. The foce exeted on the loop by the magnetic field of the wie is N towads left N towads ight 7. 4 towads ight 7. 4 towads left [Answes : () b () d (3) a (4) d] C7A MAGNETIC DIPOLE Conside a small cuent caying loop of N tuns and aea A caying a cuent I has simila patten of lines of foce as ba magnet, as shown in figue. That s why a cuent loop has magnetic dipole moment which is defined as NIA. C7B The diection of coincides with the diection of the aea vecto A. The diection A is pependicula to the plane of the loop. If we cul the finges of the ight hand along the cuent, the diection of thumb gives the diection of dipole moment. MAGNETIC DIPOLE IN A UNIFORM MAGNETIC FIELD A cuent loop of magnetic dipole in a unifom magnetic field expeiences a zeo foce but non zeo toque and the toque is given by B.

8 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 Potential enegy of the dipole When a dipole is placed in a unifom magnetic field, it posses potential enegy given by U.B Fo = U = B = / U = = U = +B PMEC 8 Hence fo = i.e. when a dipole is placed along the diection of field, the dipole is in stable equilibium wheeas fo = the dipole is in unstable equilibium. Pactice Poblems :. A conducting cicula loop of adius caies a constant cuent i. It is placed in a unifom magnetic field B such that B is pependicula to the plane of the loop. The magnetic foce, toque and potential enegy of the loop is espectively,, i B,, Bi,, i B Bi,, i B [Answes : () a] C8 AMPERE S LAW Ampee s law states that the line integal of B aound any closed path equals times the net cuent (I) though the aea enclosed by the path i.e. B.dl I. Using Ampee s law, one finds that the field inside a toodal coil and solenoid ae NI B (tooid) N B I ni (solenoid) l whee N is the total numbe of tuns, n is the numbe of tuns pe unit length and is the adius of the tooidal coil. Pactice Poblems :. A hollow cylinde of adius caies a cuent I. Let the magnetic field inside the cylinde is B and outside the cylinde is B. Then B =, B B, B B =, B B, B =. A solid cylinde of adius caies a cuent I. Let the magnetic field fom the axis of the cylinde is B. Which of the following gaph will epesent the vaiation of B with the distance (x) fom the axis of the cylinde? [Answes : () a () c] C9 Magnetism : Thee ae two types of magnetic poles known as Noth and South pole. Howeve, evey effot to isolate the poles of a magnet have failed. Thus a magnetic monopole does not exist. Pole Stength : In the study of ba magnets it is sometimes useful to intoduce a quantity called magnetic pole stength (q m ) which is analogous to chage in electostatics. In tems of q m the magnetic moment M of ba magnet of length l can be witten as m = l q m. The unit of magnetic moment is Am o J/T.

9 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 Pactice Poblems : PMEC 9. A ba magnet of magnetic moment M is cut into two pats of equal length. The magnetic moment of eithe pat is M M M/ zeo [Answes : () c] C Popeties of electic and magnetic dipoles Popety Electic Dipole Magnetic Dipole p m Field at distant point along axis E B x Field at distant point along pependicula bisecto (boad-side-on position) E x p m B x 4 x Foce in an extenal unifom field zeo zeo Toque in an extenal field p E m B potential enegy in an extenal field p. E m.b Wok done in otating the dipole in an p E ( cos ) mb( cos ) extenal field fom the equilibium position Pactice Poblems :. A magnetic needle lying paallel to a magnetic field equies W units of wok to tun it though 6. The toque equied to maintain the needle in this position is 3 3 W W W W. The magnetic field at a point A on the axis of a small ba magnet is equal to the field at a point B on the equato of the same magnet. The atio of the distances of A and B fom the cente of the magnet is 3 /3 3 /3 [Answes : () a () d] C Time peiod of small oscillations of a magnet in a magnetic field : Vibation Magnetomete Suppose a magnet of dipole moment m is suspended in a unifom magnetic field B. If it is given a slight otation fom its position of equilibium, the estoing toque will be = mb sin = mb Theefoe the magnet will oscillate with a time peiod : T the magnet. Pactice Poblems : I mb, whee I is the moment of inetia of. The time peiod of oscillation of a feely suspended magnet is 4 s. It it is boken in length into two equal pats and one pat is suspended in the same way, its time peiod will be 4 s s.5 s.5 s. The time peiod of oscillation of a ba magnet suspended hoizontally along the magnetic meidian is T. If this magnet is eplaced by anothe magnet of the same size and pole stength, but with double the mass, the new time peiod will be T / T / T T [Answes : () b () c]

10 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC C Gauss s Law of Magnetism The law states that B.dS fo all closed sufaces. This is a pecise expession of the fact that magnetic C3 monopoles do not exist. The Magnetic Field of the Eath Vaious obsevations indicate that thee is a magnetic field associated with the eath. The field is appoximately like that of a fictious huge ba magnet located deep inside the eath with its noth pole nealy towads the geogaphic south and the south pole nealy towads the geogaphic noth. The actual souce of the field appeas to be some molten chaged metallic fluid giving ise to a cuent flowing inside the coe of the eath. Geogaphic meidian : It is the vetical plane passing though the axis of otation of the eath. Magnetic meidian : It is the vetical plane passing though the axis of a feely suspended magnet. Declination : It is the angle between the geogaphic meidian and the magnetic meidian at a place. Declination vaies iegulaly fom place to place. Dip () : It is the angle between the eath s magnetic field and the hoizontal diection at a place. It is at the magnetic equato and 9 at the poles, vaying gadually as one goes fom equato to poles. We have BV tan, whee B B H and B V ae the hoizontal and vetical components of eath s field B. H Pactice Poblems :. At a cetain place the hoizontal component of eath s magnetic field is 3 times the vetical component. The angle of dip at that place is [Answes : () d] C4 Magnetic Popeties of Mateials : On the basis of magnetic behaviou, all the mateials can be classified into thee categoies :. diamagnetic,. Paamagnetic, 3. Feomagnetic.. Diamagnetic substances ae those which ae feebly epelled by a magnet. When placed in a non-unifom magnetic field, they tend to move fom stonge to weake pats of the field. Examples : Bi, Cu, Zn, Hg, Au, Pb, NaCl, H O etc. In fact, most of the mateials ae diamagnetic.. Paamagnetic substances ae those which ae feebly attacted by a magnet. When placed in a non-unifom field they tend to move fom weake to stonge pats of the field. Examples : Al, Na liquid O, CuCl, wood etc. 3. Feomagnetic substances ae those which ae stongly attacted by a magnet. Examples : Fe, Ni, Co etc. C5 Cuie Law The vaiation of magnetic moment pe unit volume, M, also called magnetisation, as a function of B/T, whee T is the tempeatue and B is the magnetic field fo low value of B/T is given by, M B/T o CB M, whee C is a constant. This is called the Cuie law. T

11 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC Cuie Tempeatue : It is that tempeatue above which the feomagnetic mateial becomes paamagnetic. Fo ion the Cuie tempeatue is 43 K. C6 Relative Pemeability ( ) and Magnetic Susceptibility ( ) Relation between Relative Pemeability ( ) and Magnetic Susceptibility is given by = + C7 Mateial Diamagnetic slightly less than unity small, negative Paamagnetic slightly moe than unity small, positive Feomagnetic much geate than unity (~ 3 ) lage, positive. Hysteesis : When a piece of feomagnetic mateial is taken though a cycle of magnetisation, the vaiation of magnetic induction B with the magnetic intensity H is as shown in the diagam. The value of B at which H (magnetic intensity) is zeo is called emanence (B ). The value of H at which B (magnetic field) is zeo is called coecivity. The complete cycle of magnetisation is known as hysteesis loop. The following impotant points concening hysteesis loop should be noted :. The enegy spent pe cycle in taking a feomagnetic mateial though a cycle of magnetisation is popotional to the aea of the hysteesis loop. This aea is vey small fo soft ion and is lage fo steel. Theefoe soft ion is useful fo coes of tansfomes and geneatos.. Fo steel, coecivity is vey lage and emanence is faily lage.theefoe, steel is used fo making pamanent magnets. The aea of the loop is lage fo steel, but it does not matte because a pemanent magnet has not to be taken though a cycle of magnetisation. Fo soft ion coecivity is small and aea of the loop is also small. Theefoe it is a suitable mateials fo making electomagnets. Pactice Poblems :. Electomagnets ae made of soft ion because soft ion has low susceptibility and low etentivity high susceptibility and high etentivity high susceptibility and low etentivity low pemeability and high etentivity. The aea of the B-H hysteesis loop is an indication of the pemeability of the mateial susceptibility of the mateial etentivity of the mateial enegy dissipated pe cycle 3. The mateial of a pemanent magnet has high etentivity, low coecivity low etentivity, high coecivity low etentivity, low coecivity high etentivity, high coecivity [Answes : () c () d (3) d]

12 PMEC INITIAL STEP EXERCISE (OBJECTIVE). In a moving coil galvanomete the cuent i is elated to the deflection as i = n, whee n is a constant. The value of n is ½ ½. To make the field adial in a moving coil galvanomete the numbe of tuns in the fom of inceased magnet is taken in the fom of hose-shoe poles ae cylindically cut coil is wound on aluminium fame 3. Choose the coect statement fo magnetic lines of foce 6. All the magnetic mateials lose thei magnetic popeties when dipped in wate dipped in oil bought nea a piece of ion stongly heated 7. Which of the following is most suitable fo the coe of an electomagnet? ai soft ion steel Cu-Ni alloy 8. If a diamagnetic solution is poued into a U-type and one am of this U-tube placed between the poles of a stong magnet, with the meniscus in a line with the field, then the level of the solution will cannot intesect at all ise fall In the case of a ba magnet, the lines of magnetic induction un continuously though the ba and outside In the case of a ba magnet, the lines of magnetic induction inside the magnet un fom south to noth pole All ae coect 4. Isogonic lines on a magnetic map have zeo angle of dip zeo angle of declination the same angle of dip the same angle of declination 5. A magnetic needle suspended by a silk thead is vibating in the eath s magnetic field. If the tempeatue of the needle is inceased by 5 C, then oscillate slowly emain as such 9. Magnet pemeability is maximum fo diamagnetic substances paamagnetic substances feomagnetic substances all of these. At the magnetic noth pole of the eath, the value of the hoizontal component of eath s magnetic field and the angle of dip ae espectively zeo, maximum maximum, minimum maximum, maximum minimum, minimum the time peiod deceases the time peiod emains unchanged the time peiod inceases the needle stops vibating Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857

13 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 3 FINAL STEP EXERCISE. A potential diffeence of 6 V is applied acoss the plates of a paallel plate capacito. The sepaation between the plates is 3 mm. A magnetic field also exists between the plates. An electon pojected paallel to the plates with a speed of 6 m/s moves undeflected between the plates. The magnitude and diection of the magnetic field is. T, into the page. T, out of the page. T, into the page. T, out of the page. A chage q coulomb is ciculating in an obit of adius metes making n evolutions pe second. The magnetic field poduced at the cente of the cicle in N/Am is 5. A chaged paticle having kinetic enegy E entes nomally a egion of unifom magnetic field between two plates P and P as shown in the figue. If the paticle just misses hitting the plate P, then the magnetic field B in the egion between the plates is q 7 n q 7 me qd me qd nq 7 n 7 q 3. In the figue x, y and z ae long staight wies. The magnetic foce on 5 cm length of y is 4 N towads ight 4 4 N towads ight 4 N towads left 4 4 towads left 4. A cicula loop of mass m and adius lies on a hoizontal table (xy-plane). A unifom magnetic field is applied paallel to the x-axis. The cuent I that should flow in the loop so that it just tilts about one point on the table is mg B mg B mg B B mg me qd me qd 6. A magnet is suspended in such a way that it oscillates in the hoizontal plane. It makes oscillations pe minute at a place whee the dip angle is 3 and 5 oscillations pe minute at a place whee the dip angle is 6. The atio of eath s total magnetic fields at the two places is 33 : 8 3 : 9 4 : 9 6 : A shot magnet of moment 6.75 Am poduces a neutal point on its axis. If the hoizontal component of eath s magnetic field is 5 5 Wb/m, then the distance of the neutal point fom the cente of the magnet is cm cm 3 cm 4 cm 8. A wie of given length is folded into a cicula coils of constant adius. A constant cuent is flowing though the loop. The magnetic field poduced at the cente of the coil is diectly popotional to the numbe of tuns as n. The value of is 3 9. In the above poblem the magnetic dipole moment of the loop depends on numbe of tuns as n. The value of is 3

14 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 ANSWERS (INITIAL STEP EXERCISE). a. c 3. d 4. d 5. c 6. d 7. b 8. b 9. c. a PMEC 4 ANSWERS (FINAL STEP EXERCISE). d. c 3. b 4. c 5. d 6. d 7. c 8. c 9. a AIEEE ANALYSIS []. If a cuent is passed though a sping, then the sping will expand compess emains same none of these. In an electon and a poton hving same momenta ente pependicula to a magnetic field, then cuved path of electon and poton will be same (ignoing the sense of evolution) they will moe undeflected cuved path of electon is moe cuved than that of poton path of poton is moe cuved 3. If in a cicula coil A of adius R, cuent i is flowing and in anothe coil B of adius R a cuent i is flowing, then the atio of the magnetic fields, B A and B B povided by them will be / 4 4. At a specific instant emission of adioactive compound is deflected in a magnetic field. The compound can emit (i) electons (ii) potons (iii) He + (iv) neutons The emission at the instant can be (i), (ii), (iii) (i), (ii), (iii), (iv) (iv) (ii), (iii) ii ii ii ii 4 dl tan dl sin dl cos dl sin 6. The time peiod of a chaged paticle undegoing a cicula motion in a unifom magnetic field is independent of its speed mass chage magnetic induction 5. Wies and caying cuents i and i espectively ae inclined at an angle to each othe. What is the foce on a small element dl of wie at a distance fom wie (as shown in figue) due to the magnetic field of wie?

15 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 5 AIEEE ANALYSIS [3] 7. A paticle of chage 6 8 coulomb moving with velocity ms along the x-axis entes a egion whee a magnetic field of induction B is along the y-axis, and an electic field of magnitude 4 V/m is along the negative z-axis. If the chaged paticle continues moving along the x-axis, the magnitude of B is 6 Wb/m 3 Wb/m 3 Wb/m 5 Wb/m 8. A thin ectangula magnet suspended feely has a peiod of oscillation equal to T. Now it is boken into two equal halves (each having half of the oiginal length) and one piece is made to oscillate feely in the same field. If the peiod of oscillation is T, the atio T T is /4 / / 9. A magnetic needle lying paallel to a magnetic field equies W units of wok to tun it though 6. The toque needed to maintain the needle in this position will be 3 W W 3 W W 3. A cuent i ampee flows along an infinitely long staight thin walled tube then the magnetic induction at any point inside the tube is infinite zeo 4 i tesla i tesla [4] 4. A long wie caies a steady cuent. It is bent into a cicle of one tun and the magnetic field at the cente of the coil is B. It is then bent into a cicula loop of n tuns. The magnetic field at the cente of the coil will be n B n B n B n B [4]. The magnetic lines of foce inside a ba magnet depend upon the aea of coss-section of the ba magnet ae fom south-pole to noth-pole of the magnet ae fom noth-pole to south-pole of the magnet do not exist. Cuie tempeatue is the tempeatue above which a feomagnetic mateial becomes dia magnetic a paamagnetic mateial becomes feo magnetic a feomagnetic mateial becomes paa magnetic a paamagnetic mateial becomes dia magnetic. A paticle of mass M and chage Q moving with velocity v descibes a cicula path of adius R when subjected to a unifom tansvese magnetic field of induction B. The wok done by the field when the paticle completes one full cicles is BQR BQvR Mv R R zeo AIEEE ANALYSIS [4/5] 5. The magnetic field due to a cuent caying cicula loop of adius 3 cm at a point on the axis at a distance of 4 cm fom the cente is 54 T. What will be its value at the cente of the loop? 5 T 5 T 5 T 75 T [4] 6. Two long conductos, sepaated by a distance d cay cuent l and l in the same diection. They exet a foce F on each othe. Now the cuent in one of them is inceased to two times and its diection is evesed. The distance is also inceased to 3d. The new value of the foce between them is F F/3 F/3 F/3 [4]

16 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 6 7. The length of a magnet is lage compaed to its width and beath. The time peiod of its oscillation in a vibation magnetomete is s. The magnet is cut along its length into thee equal pats and thee pats ae then placed on each othe with thei like poles togethe. The time peiod of this combination will be s /3 s 3 s /3 s [4] 8. The mateials suitable fo making electomagnets should have high etentivity and high coecivity low etentivity and low coecivity high etentivity and low coecivity low etentivity and high coecivity [4] 9. Two thin, paallel wies, sepaated by a distance d cay a cuent of i A in the same diection. They will attact each othe with a foce of i / (d ) epel each othe with a foce of i / (d) attact each othe with a foce of i / (d) epel each othe with a foce of i / (d ) [5]. Two concentic coils each of adius equal to cm ae placed at ight angle to each othe. 3 ampee and 4 ampee ae the cuents flowing in each coil espectively. The magnetic induction in Webe/m at the cente of the coils will be ( = 4 7 Wb / A. m) [5]. A chaged paticle of mass m and chage q tavels on a cicula path of adius that is pependicula to a magnetic field B. The time taken by the paticle to complete one evolution is qb m mq B m qb q B m [5]. A magnetic needle is kept in a non-unifom magnetic field. It expeiences a foce and a toque a foce but not a toque a toque but not a foce neithe a foce no a toque [5] 3. A unifom electic field and a unifom magnetic field ae acting along the same diection in a cetain egion. If an electon is pojected along the diection of the fields with a cetain velocity then it will tun towads ight of diection of motion it will tun towads left of diection of motion its velocity will decease its velocity will incease [5] AIEEE ANALYSIS [6] 4. In a egion, steady and unifom electic and magnetic fields ae pesent. These two fields ae paallel to each othe. A chaged paticle is eleased fom est in this egion. The path of the paticle will be ellipse cicle helix staight line 5. A long solenoid has tuns pe cm and caies a cuent i. The magnetic field at its cente is 6.8 Webe/m. Anothe long solenoid has tuns pe cm and its caies a cuent i/3. The value of the magnetic field at its cente is.5 3 Webe/m.5 4 Webe/m.5 Webe/m.5 5 Webe/m 6. Needles N, N and N 3 ae made of a feomagnetic, a paamagnetic and a diamagnetic substance espectively. A magnet when bought close to them will attact N stongly, but epel N and N 3 weakly attact all thee of them attact N and N stongly but epel N 3 attact N stongly, N weakly and epel N 3 weakly

17 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 7 AIEEE ANALYSIS [7] 7. A chaged paticle with chage q entes a egion of constant, unifom and mutually othogonally field E and B with a velocity v pependicula to both E and B, and comes out without any change in magnitude o diection of v. Then v BE / E v E B / B v B E / B v E B / E 8. A long staight wie of adius a caies a steady cuent I. The cuent is unifomly distibuted acoss its coss-section. The atio of the magnetic fields at a and a is 4 9. A cuent I flows along the length of an infinitely long, staight, thin walled pipe. Then the magnetic field at all points inside the pipe is the same, but not zeo the magnetic field is zeo only on the axis of the pipe the magnetic field is diffeent points inside the pipe the magnetic field at any point inside the pipe is zeo 4 3. A chaged paticle moves though a magnetic field pependicula to its diection. Then kinetic enegy changes but he momentum is constant the momentum changes but the kinetic enegy is constant both momentum and kinetic enegy of the paticle ae constant. both, momentum and kinetic enegy of the paticle ae constant. 3. Two identical conducting wies AOB and COD ae placed at ight angles to each othe. The wies AOB caies an electic cuent I and COD caies a cuent I. The magnetic field on a point lying at a distance d fom O, in a diection pependicula to the plane of the wies AOB and COD, will be given by I I d I I d / I I / d I I d ANSWERS AIEEE ANALYSIS. b. a 3. a 4. a 5. c 6. a 7. c 8. d 9. c. b. c. d 3. b 4. b 5. a 6. c 7. a 8. b 9. c. a. b. a 3. c 4. d 5. c 6. d 7. c 8. d 9. d 3. b 3. d

18 Einstein Classes, Unit No., 3, Vadhman Ring Road Plaza, Vikas Pui Extn., Oute Ring Road New Delhi 8, Ph. : , 857 PMEC 8 TEST YOURSELF. A dip cicle is at ight angles to the magnetic meidian. The appaent dip is Which of the following in motion can NOT be deflected by magnetic fields? Potons Cathode ays Alpha paticle Neutons 3. A poton of enegy MeV descibes a cicula path in a plane at ight angles to a unifom magnetic field of T. The mass of the poton is.7 7 kg. The cycloton fequency of the poton is vey nealy equal to 4 Hz 5 Hz 6 Hz 7 Hz 4. The foce F expeienced by a paticle of chage q moving with a velocity v in a magnetic field B is given by F = q( v B ). Which pais of vectos ae at ight angles to each othe? F and v F and B v B and v all 5. A staight hoizontal conducting od of length.5 m and mass 5 g is suspended by two vetical wies at its ends. A cuent of 5. A is set up in the od though the wies. What magnetic field should be set up nomal to the conducto in ode that the tension in the wies is zeo? Ignoe the mass of the wies and take g = ms.. T. T.3 T.4 T 6. Two cicula cuent caying coils of adii 3 cm and 6 cm ae each equivalent to a magnetic dipole having equal magnetic moment. The cuents though the coils ae in the atio of : : : 4 : 7. An electon of chage e moves in a cicula obit of adius aound a nucleus. The magnetic field due to obital motion of the electon at the site of the nucleus is B. The angula velocity of the electon is eb 4 4B e eb B e 8. The most suitable metal fo making pemanent magnets is ion steel coppe aluminium 9. A cicula coil of n tuns and aea of coss-section A, caying a cuent i, ests with its plane nomal to an extenal magnetic field B. The coil is fee to tun about an axis in its plane pependicula to the field diection. If the moment of inetia of the coil about its axis of otation is I, its fequency of oscillation about its stable equilibium is given by f f f f. d. d 3. a 4. d 5. b niab I nia BI iab ni / / / niab i /. A magnetized wie of magnetic moment M is bent into an ac of a cicle that subtends an angle of 6 at the cente. The equivalent magnetic moment is M 3M M 4M 6. d 7. c 8. b 9. a. c ANSWERS