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OBJECTIVE UNSOLVED LEVEL - I 1. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is. (a) μ0 NI b μ 0 NI b (b) 2μ0 NI a μ0 IN b (c) 2b aln a (d) b a ln a . 2. Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are vA and vB respectively and the trajectories are as shown in the figure then (a) mAvA < mBvB (b) mAvA > mBvB (c) mA < mB and vA < vB (d) mA = mB and vA = vB. 3. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the +z direction, then (a) positive ions deflect towards +y direction and negative ions towards -y direction (b) all ions deflect towards +y direction (c) all ions deflect towards -y direction (d) positive ions deflect towards -y direction and negative ions towards +y direction. 4. An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR. The magnetic field due to this current at the point M is H1. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, the current in PQ remaining unchanged. The mag- netic field at M is now H2. The ratio H1/H2 is given by: (a) 1/2 (b) 1 (c) 2/3 (d) 2. - P I 900 Q M 900 S + R - 5. A circular loop of radius R, carrying current I, lies in xy plane with its centre at origin. The total magnetic flux through xy plane is: (a) directly proportional to I (b) directly proportional to R (c) inversely proportional to R (d) zero. 6. A particle is moves in a circular path of diameter 1.0 m under the action of magnetic field of 0.40 Tesla. An electric field of 200 V/m makes the path of particle straight. Find the charge / mass ratio of the particle (a) (c) 2.5 105 C/kg 3.5 105 C/kg (b) (d) 2 105 C/kg 3 105 C/kg . 7. A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a (a) straight line (b) circle (c) helix (d) cycloid. 8. A proton, a deutron and an α -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rP, rd and r α denote respectively the radii of the trajec- tories of these particles then (a) (c) rα rp rd rα rd rp (b) (d) rα rd rp rp rd rα . 9. Two thin long parallel wires separated by a distance b are carrying a current i amp. each. The magnitude of the force per unit length exerted by one wire on the other is (a) μ0i2 b2 (b) 2 0 2πb (c) μ0i (d) 2πb μ0i . πb2 10. A charged particle of mass m and charg

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OBJECTIVE UNSOLVED LEVEL - I 1. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is. (a) μ0 NI b μ 0 NI b (b) 2μ0 NI a μ0 IN b (c) 2b aln a (d) b a ln a . 2. Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are vA and vB respectively and the trajectories are as shown in the figure then (a) mAvA < mBvB (b) mAvA > mBvB (c) mA < mB and vA < vB (d) mA = mB and vA = vB. 3. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the +z direction, then (a) positive ions deflect towards +y direction and negative ions towards -y direction (b) all ions deflect towards +y direction (c) all ions deflect towards -y direction (d) positive ions deflect towards -y direction and negative ions towards +y direction. 4. An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR. The magnetic field due to this current at the point M is H1. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, the current in PQ remaining unchanged. The mag- netic field at M is now H2. The ratio H1/H2 is given by: (a) 1/2 (b) 1 (c) 2/3 (d) 2. - P I 900 Q M 900 S + R - 5. A circular loop of radius R, carrying current I, lies in xy plane with its centre at origin. The total magnetic flux through xy plane is: (a) directly proportional to I (b) directly proportional to R (c) inversely proportional to R (d) zero. 6. A particle is moves in a circular path of diameter 1.0 m under the action of magnetic field of 0.40 Tesla. An electric field of 200 V/m makes the path of particle straight. Find the charge / mass ratio of the particle (a) (c) 2.5 105 C/kg 3.5 105 C/kg (b) (d) 2 105 C/kg 3 105 C/kg . 7. A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a (a) straight line (b) circle (c) helix (d) cycloid. 8. A proton, a deutron and an α -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rP, rd and r α denote respectively the radii of the trajec- tories of these particles then (a) (c) rα rp rd rα rd rp (b) (d) rα rd rp rp rd rα . 9. Two thin long parallel wires separated by a distance b are carrying a current i amp. each. The magnitude of the force per unit length exerted by one wire on the other is (a) μ0i2 b2 (b) 2 0 2πb (c) μ0i (d) 2πb μ0i . πb2 10. A charged particle of mass m and charg

- 1. OBJECTIVE UNSOLVED LEVEL - I 1. A coil having N turns is wound tightly in the formof a spiral with inner and outer radii a and b respectively. Whena current I passes through the coil, the magnetic field at the centre is. (a) b NI μ0 (b) a NI μ 2 0 (c) a b ln a b 2 NI μ0 (d) 0 ln . IN b b a a A B 2. Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are vA and vB respectively and the trajectories are as shown in the figure then (a) mA vA < mB vB (b) mA vA > mB vB (c) mA < mB and vA < vB (d) mA = mB and vA = vB . 3. An ionized gas contains both positive and negative ions. Ifit is subjected simultaneouslyto an electric field alongthe +x directionand a magnetic field along the+z direction, then (a) positive ionsdeflect towards +ydirectionand negative ions towards -ydirection (b) allions deflect towards +ydirection (c) allions deflect towards -ydirection (d) positive ionsdeflect towards -ydirectionand negative ions towards+ydirection. M R S I P 900 900 Q - - + 4. An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR. The magnetic field due to this current at thepoint M is H1 . Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, the current in PQ remaining unchanged. The mag- netic field at M is now H2 . The ratio H1 /H2 is given by: (a) 1/2 (b) 1 (c) 2/3 (d) 2. 5. A circular loop of radius R, carrying current I, lies in xyplane with its centre at origin. The total magnetic fluxthroughxyplaneis: (a) directlyproportionalto I (b) directlyproportionalto R (c) inverselyproportionalto R (d) zero. 6. A particle is moves in acircular path ofdiameter 1.0 munder theaction ofmagnetic field of0.40 Tesla.Anelectric field of200V/mmakes the pathofparticle straight. Find the charge / mass ratio ofthe particle (a) 5 2.5 10 /kg C (b) 5 2 10 /kg C (c) 5 3.5 10 /kg C (d) 5 3 10 /kg C .
- 2. 7. A charged particle is released fromrest in a regionof steady and uniformelectric and magnetic fields whichare parallelto eachother. The particle willmove in a (a) straight line (b) circle (c) helix (d) cycloid. 8. A proton, a deutron and an α -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. IfrP , rd and rα denoterespectivelythe radiiofthe trajec- tories ofthese particles then (a) d p α r r r (b) p d α r r r (c) p d α r r r (d) α d p r r r . 9. Two thin long parallel wires separated by a distance b are carrying a current i amp. each. The magnitude oftheforce per unit lengthexerted byone wire onthe other is (a) 2 2 0 b μ i (b) b π 2 μ 2 0i (c) b π 2 μ0i (d) 2 0 b π μ i . 10. A charged particle ofmass mand charge q enters amagnetic field B witha velocity v at an angle θ withthe direction ofB. Theradius ofthe resultingpath is (a) B θ sin q mv (b) θ sin B q mv (c) B q mv (d) B θ tan q mv . 11. Anelectronfallingfreelyundergravityentersaregionofuniformhorizontalmagnetic fieldpointing north to south. The particle willbe deflected towards (a) east (b) west (c) north (d) south. 12. A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and having a charge 5 1.0 10 C be projected from south to north so that it moves with a uniform velocity (a) 48 m/s (b) 49 m/s (c) 47 m/s (d) 50 m/s 13. In a region of space uniform electric field is present as j ˆ E E 0 and uniform magnetic field is present as k̂ . B B 0 . An electron is released from rest at origin. Which of the following best represents the path followed by electron after release.
- 3. x y (a) x y (b) x y (c) (d) Z y A 14. The negatively charged disc in figure is rotated clock-wise. What is the direction of the magnetic field at point A in the plane of the disc? (a) Into the page (b) Out of the page (c) Up the page (d) Down the page. 15. Which of the following particle will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field? (a) electron (b) proton (c) He+ (d) Li+ .
- 4. OBJECTIVE UNSOLVED LEVEL - II 1. Aparticle ofmass mand chargeq moves withaconstant velocityvalongthe positive x-direction. It enters a region containing a uniformmagnetic field B directed along the negative z direction, extending fromx= a to x= b. The minimumvalue ofv required so that the particle can just enter the region x> b is (a) qb B/m (b) q (b-a)B/m (c) qa B/m (d) q(b+a) B/2m. 2. Along straight wire along the z-axiscarries a current Iinthe negative zdirection. The magnetic vector field B at a point having coordintes (x, y) in the z = 0 plane is: (a) 0 2 2 ˆ ˆ I(yi xj) 2 (x y ) (b) 0 2 2 ˆ ˆ I(yi xj) 2 (x y ) (c) 0 2 2 ˆ ˆ I(xj yi) 2 (x y ) (d) 0 2 2 ˆ ˆ I(xj yi) 2 (x y ) . x y z 2a 3. A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic filed due to this loop at the point P (a, 0, a) points in the direction. (a) 1 ˆ ˆ ( j k) 2 (b) 1 ˆ ˆ ˆ ( j k i) 3 (c) 1 ˆ ˆ ˆ (i j k) 3 (d) 1 ˆ ˆ (i k) 2 . 4. A long, straight wire carries a current along the Z-axis. One can find two points in the X-Y plane such that (a) the magnetic fields are equal (b) the directions of the magnetic fields are the same (c) the magnitudes of the magnetic fields are equal (d) the field at one point is opposite to that at the other point. 5. In a coaxial, straight cable, the central conductor and the outer conductor carrry equal currents in opposite directions. The magnetic field is zero. (a) outside the cable (b) inside the inner conductor (c) inside the outer conductor (d) in between the two conductors. 6. Two parallel, long wires carry currents i1 and i2 with i1 > i2 . When the currents are in the same direction, the magnetic field at a point midway between the wires is 90 T . If the direction of is reversed, the field becomes 30 T . The ratio 1 2 i /i is (a) 4 (b) 3 (c) 2 (d) 1.
- 5. 7. Two long parallelwires are at a distane 2d apart. Theycarrysteadyequalcurrents flowing out of the plane ofthe paper, as shown. The variationofthe magnetic field B alongthe line XX' is given by: (a) x ' x B d d (b) x ' x B d d (c) x ' x B d d (d) x ' x d d . 8. Two insulated rings, one of slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady cur- rent is set up in each of them. (a) the two rings rotate into acommonplane (b) the innerring oscillatesabout itsinitialposition (c) the outerring stays stationarywhile the inner one moves into the plane ofthe outer ring (d) the innerring stays stationarywhile the outer one moves into the plane ofthe inner ring. 9. A charged particle goes undeflected in a region containing electric and magnetic field. It is possible that (a) E||B, v || E (b) E is not parallel to B (c) v||B but E is not parallel to B (d) E || B but v is not parallel to E . 10. A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to (a) the velocity (b) the momentum (c) the kinetic energy (d) none of these. 11. The magnetic field at the origin due to a current element idl placed at a position r is (a) 0 3 i d r 4 r l (b) 0 3 i r d 4 r l (c) 0 3 i r d 4 r l (d) 0 3 i d r 4 r l .
- 6. 12. A proton of mass 1.67 × 10-27 kg and charge 1.6 × 10-19 C is projected with a speed of 2 × 106 m/s at an angle of 600 to the X-axis in XY plane. If a uniform magnetic field of 0.104 tesla is applied along the Y-axis, the path ofthe proton is (a) a circle of radius 0.1 mand time period 7 10 s (b) a circle of radius 0.2 mand time period s 10 π 7 (c) a helix ofradius 0.1 mand time period s 10 π 2 7 (d) a helix ofradius 0.2 mand time period s 10 π 4 7 . 13. Apotential difference of 500 V is applied across a parallel plate capacitor. The separation be- tween the plates is 2×10-3 m. The plates of the capacitor are vertical. An electron is projected verticallyupwards betweenthe plateswitha velocityof105 m/sand it movesundeflected between the plates. The magnetic field acting perpendicular to the electric fieldhas magnitude of (a) 0 Wb/m2 (b) 2.5 Wb/m2 (c) 3.0 Wb/m2 (d) 5.0 Wb/m2 . 14. Two similar coaxial coils, separated bysome distance, carrythe same current I but in opposite directions. The magnitude ofthe magneticfield B at apoint onthe axis at the mid point ofthe line joining the centre is : (a) zero (b) the same as that produced byone coil (c) twice that produced byone coil (d) halfofthat produced byone coil. O Y C R R B R X I I A R 15. Conductor ABC consist of two quarter circular path of radius R lies in X-Y plane and carries current I as shown. A uniform mag- netic field B is switched on in the region that exert force F = 2 IRB0 k̂ on conductor ABC. B can be (a) ) î ( B 2 0 (b) 0 ˆ 2 B i (c) ) ĵ î ( 2 B0 (d) both (b) and (c).