16 - MAGNETIC EFFECTS OF CURRENTS Page 1 ( Answers at the end of all questions )

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1 16 - MAGNETIC EFFECTS OF CURRENTS Page 1 1 ) One conducting U tue can slide inside another as shown in the figure, aintaining electrical contacts etween the tues. The agnetic field B is perpendicular to the plane of the figure. If each tue oves towards the other at a constant speed V, then the ef induced in the circuit in ters of B, l and V where l is the width of each tue, will e - BlV BlV BlV zero [ AIEEE 005 ] ) Two thin, long, parallel wires, separated y a distance d c rry a current i A in the sae direction. They will i repel each other with a force of o attract eac other with a force of oi πd πd oi oi repel each other with a force of at ract each other with a force of πd πd [ AIEEE 005 ] 3 ) A charged particle of ass and charge q travels on a circular path of radius r that is perpendicular to a agnetic field B. T e tie taken y the particle to coplete one revolution is πq B πq π πqb ( c [ AIEEE 005 ] B qb 4 ) A unifor electric field and a un or agnetic field are acting along the sae direction in a certain region. If an el ct on is projected along the direction of the fields with a certain velocity, then its velocity will increase its velocity will decrease it will turn owards left of direction of otion it will turn t wards right of direction of otion. [ AIEEE 005 ] 5 ) Two concent ic c ils each of radius equal to π c are placed at right angles to each other. 3 apere and 4 apere are the currents flowing in each coil respectively. The ag etic induction in weer / at the centre of the coils will e ( 0 = 4π 10-7 W / A ) ( a [ AIEEE 005 ] 6 ) A current I apere flows along an infinitely long straight thin walled tue, then the agnetic induction at any point inside the tue is i infinite zero 0 i. tesla tesla [ AIEEE 004 ] 4π r r 7 ) A long wire carries a steady current. It is ent into a circle of one turn and the agnetic field at the centre of the coil is B. It is then ent into a circular loop of n turns. The agnetic field at the centre of the coil will e nb n B nb n B [ AIEEE 004 ]

2 16 - MAGNETIC EFFECTS OF CURRENTS Page 8 ) The agnetic field due to a current carrying circular loop of radius 3 c at a point on the axis at a distance of 4 c fro the centre is 54 T. What will e its value at the centre of the loop? 50 T 150 T 15 T 75 T [ AIEEE 004 ] 9 ) Two long conductors, separated y a distance d carry currents Ι 1 and Ι in th sae direction. They exert a force F on each other. Now the current in one f the is increased to two ties and its direction is reversed. The distance is also increased to 3d. The new value of the force etween the is - F F / 3 - F / 3 - F / 3 [ AIEEE 004 ] 10 ) A particle of ass and charge q oving with velocity v des ries a circular path of radius r when sujected to a unifor transverse agnetic f eld of induction B. The work done y the field, when the particle copletes o e full circle, is zero π v πvqb πrqb [ AIEEE 003 ] 11 ) A part of a long wire carrying a current I is en into a circle of radius r as shown in the f gure. The net agnetic field at the centre O of the circular oop is 0 Ι 0 Ι 0 Ι ( 1+ π ) ( d 0 Ι ( π - 1) 4r r πr πr [ AIEEE 00 ] 1 ) An electron oving with a speed u along the positive x-axis at y = 0 enters a region of unifor agnetic field ^ B = B 0 hich exists to the right of y-axis. The elect on exits fro the region after soe tie with he speed v at ordinate y, then v > u, y < 0 v = u, y > 0 v > u, y > 0 v = u, y < 0 [ IIT 004 ] 13 ) A c nduct ng loop carrying a current I is place in a unifor agnetic field pointing into the plane of the paper as shown. The loop will have a tendency to contract expand ove towards positive x-axis ove towards negative x-axis [ IIT 003 ] 14 ) A short-circuited coil is placed in a tie-varying agnetic field. Electrical power is dissipated due to the current induced in the coil. If the nuer of turns were to e quadrupled and the wire radius halved, the electrical power dissipated would e halved the sae douled quadrupled [ IIT 00 ]

3 16 - MAGNETIC EFFECTS OF CURRENTS Page 3 15 ) A current carrying loop is placed in a unifor agnetic field in four different orientations, I, II, III and IV. Arrange the in a decreasing order of potential energy. I > III > II > IV I > II > III > IV I > IV > II > III III > IV > I > II [ IIT 003 ] 16 ) A particle of ass and charge q oves with a constant vel city v along the positive x-direction. It enters a region containing a unifor agnet c field B directed along the negative z-direction, etending fro x = a to x =. The iniu value of v required so that the particle can just enter the region x > s qb q ( - a ) B qab q ( + a ) B [ IIT 00 ] 17) A long straight wire along the z-axis ca ries a current i in the negative z-direction. The agnetic vector field B at a poin aving coordinates ( x, y ) on the z = 0 plane is 0 i ( y i - x j ) 0 i ( x i j ) 0 i ( x j - y i ) 0 i ( x i - y j ) π ( x ) π ( x ) π ( x ) π ( x ) [ IIT 00 ] 18 ) A non-planar loop of c nducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the oop i of length a. The agnetic field due to this loop at th po nt P ( a, 0, a ) points in the direction 1 1 ^ ( - j + k ) ( - j + k + i ) 3 1 ^ 1 ( i + j + k ) ( i + k ) 3 [ IIT 001 ] 19 ) A coil having N turns is wound tightly in the for of a spiral with inner and outer radii a and respectively. When a current I passes through the coil, the agnetic field at the centre is 0 N I 0 N I a 0 ( N I - a ) ln a 0 N I ( + a ) 0 ) A etallic square loop ABCD is oving in its own plane with velocity V in a unifor agnetic field perpendicular to its plane as shown in the figure. Electric field is induced in AD, ut not in BC in BC, ut not in AD neither in AD nor in BC in oth AD and BC [ IIT 001 ] ln a [ IIT 001 ]

4 16 - MAGNETIC EFFECTS OF CURRENTS Page 4 1 ) Two particles A and B of asses A and B respectively and having the sae charge are oving in a plane. A unifor agnetic field exists perpendicular to this plane. The speeds of the particles are v A and v B respectively and the trajectories are as shown in the figure. Then A v A < B v B A v A > B v B A < B and v A < v B A = B and v A = v B [ IIT 001 ] ) Two circular coils can e arranged in any of the three situations shown in the figure. Their utual inductance will e axiu in situation axiu in situation axiu in situation the sae in all situations 3 ) A unifor ut tie-varying agnetic fiel B ( ) exists in a circular region of radius a and is direct d in o the plane of the paper as shown. The agnitude of the induced electric field at point P at a distance r fro the centre of he circular region 1 is zero decreas s as r increases as r de reases as 4 ) An infinitely long cond tor PQR is ent to for a right angle as shown. A current I flows through PQR. The agn tic field due to this current at the point M is H Now, another infinitely long conductor QS is connected to Q so that the current is I / in QR as well as in QS, the current in PQ reaining un hanged. The agnetic field at M is now H. T e ratio H 1 / H is given y 1 / 1 / 3 [ IIT 000 ] 1 r [ IIT 000 ] 5 ) A particle of charge q and ass oves in a circular orit of radius r with angular speed ω. The ratio of the agnitude f its agnetic oent to that of its angular oentu depends on ω and q ω, q and q and ω and [ IIT 000 ] 6 ) An ionized gas contains oth positive and negative ions. If it is sujected siultaneously to an electric field along the +x direction and a agnetic field along +z direction, then positive ions deflect towards +y direction and negative ions towards -y direction all ions deflect towards +y direction all ions deflect towards -y direction positive ions deflect towards -y direction and negative ions towards +y direction [ IIT 000 ]

5 16 - MAGNETIC EFFECTS OF CURRENTS Page 5 7 ) Two long parallel wires are at a distance d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the agnetic field B along the line XX is given y [ IIT 000 ] 8 ) A charged particle is released fro rest in a region of steady and unifor electric and agnetic fields which a e pa allel to each other. The particle will ove in a straight line circle helix cycloid [ IIT 1999 ] 9 ) A circular loop o radius R, carrying current I, lies in x-y plane with its centre at the origin. The total agn tic flux through x-y plane is directly proportional to I directly proportional to R directly proportional to R zero [ IIT 1999 ] 30 ) Two particles, each of ass and charge q, are attached to the two ends of a light rigid rod of length R. The rod is rotated at constant angular speed aout a p rpendicular axis passing through its centre. The ratio of the agnitudes of the gne c oent of the syste and its angular oentu aout the centre of the rod is q / q / q / q / π [ IIT 1998 ] 3 ) Two very long straight parallel wires carry steady currents I and -I respectively. The distance etween the wires id d. At a certain instant of tie, a point charge q is at a point equidistant fro the two wires in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The agnitude of the force due to the agnetic field acting on the charge on this instant is o I qv o I qv o I qv 0 [ IIT 1998 ] π d π d π d

6 16 - MAGNETIC EFFECTS OF CURRENTS Page 6 3 ) A proton, a deuteron and an α-particle having the sae kinetic energy are oving in circular trajectories in a constant agnetic field. If r p, r d and r α denote respectively the radii of the trajectories of these particles, then r α = r p < r d r α > r d > r p r α = r d < r p r p = r d = r α [ I T 1997 ] 33 ) H +, He + and O ++ all having the sae kinetic energy pass through a egion in which there is a unifor agnetic field perpendicular to their velocity. The asses of H +, He + and O ++ are 1 au, 4 au and 16 au respectively. Then H + will e deflected ost O ++ will e deflected ost H + and O ++ will e deflected equally all will e defle ted equally [ IIT 1994 ] 34 ) A current I flows along the length of an infinitely long, straight, thin-walled pipe. Then the agnetic field at all points inside the pipe is he sae, ut not zero the agnetic feld at any point inside the pipe s zero the agnetic field is zero only on the axis o the pipe the agnetic field is different at different p ints inside the pipe [ IIT 1993 ] 35 ) A icroeter has a resistance of 100 Ω and full scale range of 50 A. It can e used as a volteter or as a higher range aeter provided a resistance is added to it. Pick the correct range and resistance coination ( s ). 50 V range with 10 k Ω res stance in series 10 V range with 00 k Ω resistance in series 5 A range with 1 Ω res stan e in parallel 10 A range with 1 Ω esistance in parallel [ IIT 1991 ] 36 ) A particle of charge + q and ass oving under the influence of a unifor electric field E ^ i and a unifor agnetic field B k follows a trajectory fro P to Q as shown i the figure. The velocities at P and Q are v ^ i and - v ^. Which of the following stateent ( s ) is / a correct? 3 ( a E = v 3 Rate of work done y the electric field at P is v 3 4 qa 4 a Rate of work done y the electric field at P is zero Rate of work done y oth the fields at Q is zero [ IIT 1991 ] 37 ) Two particles X and Y having equal charges, after eing accelerated through the sae potential difference, enter a region of unifor agnetic field and descrie circular paths of radii R 1 and R respectively. The ratio of the ass of X to that of Y is ( R 1 / R ) 1/ R / R 1 ( R 1 / R ) R 1 / R [ IIT 1988 ]

7 16 - MAGNETIC EFFECTS OF CURRENTS Page 7 38 ) Two thin long parallel ires separated y a distance are carrying a current i ap. each. The agnitude of the force per unit length exerted y one wire on the other is o i i o o o i [ IIT 1986 ] π πi π 39 ) A proton oving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent electric and agne ic fields respectively, this region of space ay have E = 0, B = 0 E = 0, B 0 E 0, B = 0 E 0, B 0 [ IIT 1985 ] 40 ) A rectangular loop carrying a current I is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. I a steady current I is estalished in the wire as shown in the figure, the loop will rotate aout an axis parallel to the wire ove away fro the wire ov towards the wire reain stationary [ IIT 1985 ] 41 ) A conducting circular loop of adius r carries a constant current i. It is placed in a unifor agnetic field B o such that B o is perpendicular to the plane of the loop. The agnetic force acting o the loop is i r B o π r B o zero π i r B o [ IIT 1983 ] Answers c c d a c a c d c a d c d a c c c c a d a d a a,c c,d,c a,,d c a,,d c 41 c

CHAPTER 21 MAGNETIC FORCES AND MAGNETIC FIELDS

CHAPTER 21 MAGNETIC FORCES AND MAGNETIC FIELDS PROBLEMS 5. SSM REASONING According to Equation 21.1, the agnitude of the agnetic force on a oving charge is F q 0 vb sinθ. Since the agnetic field points