Electromagnetic Induction-04-OBJECTIVE UNSOLVED LEVEL - I

OBJECTIVE UNSOLVED LEVEL - I 1. The flux linked with a coil changes with time according to the equation   at2  bt  c . Then S I unit of a is : (a) Volt (b) Volt / sec (c) Volt. sec (d) Weber. 2. Lenz’s law is consistent with law of conservation of (a) current (b) emf (c) energy (d) all of the above. 3. A charged particle entering into a uniform magnetic field from outside in a direction perpendicular to the field (a) can never complete one rotation inside the field (b) may or may not complete one rotation in the field depending on its angle of entry into the field (c) will always complete exactly half of a rotation before leaving the field (d) may follow a helical path depending on its angle of entry into the field. 4. The magnetic flux linked with a coil is  and the emf induced in it is  . (a) If  = 0,  must be 0 (b) If   0 ,  cannot be 0 (c) If  is not 0,  may or may not be 0 (d) None of the above is correct. 5. A metal ring is placed in a uniform magnetic field, with its plane  to the field. If the magnitude of the field begins to change with time, the ring will experience (a) a net force (b) a torque about its axis (c) a torque about a diameter (d) a tension along its length. 6. There will be no induced emf in a straight conductor moving in a uniform magnetic field, if : (a) it is moving parallel to magnetic field (b) it is moving along its length (c) it is moving in the magnetic field with its length parallel to field then correct statement (s) is / are : (a) a only (b) a, b only (c) a, c only (d) a, b, c. x 7. Consider the situation shown in figure. If the current I in the long straight wire xy is increased at a steady rate the induced current in loop A and B will be : (a) clockwise in A and anticlockwise in B (b) anticlockwise in A and clockwise in B y (c) clockwise in both A and B (d) anticlockwise in both A and B. 8. A metallic ring is held horizontal and a magnet is allowed to fall vertically through it with N-pole pointing upwards. The acceleration of magnet near the ring is a. Then (a) a = g (b) a < g while approaching but a > g while receding (c) a < g while approaching as well as receding (d) a > g while approaching but a < g while receding. 9. The current in a L – R circuit in a time t = 2L/R reduces to (a) 36.5% of maximum (b) 13.5% of maximum (c) 0.50% of maximum (d) 63.2% of maximum. 10. A field of 5104 /  ampere-turns / meter acts at right angle to a coil of 50 turns of area 102 m2 . The coil is removed from the field in 0.1 second. Then the induced emf in the coil is : (a) 0.1 V (b) 80 KV (c) 7.96 V (d) none of the above. 11. The flux linked with a coil is 0.8 Wb when 2A current flows through it. If this current begins to increase at the rate of 0.4 A/s, the emf induced in the coil will be (a) 0.02 V (b) 0.04 V (c) 0.08 V (d) 0.16 V. 12. A non-conducting ring of radius r has charge Q. A magnetic field perpendicular to the plane of the dB ring changes at the rate dt . The torque experienced by the ring is : (a) zero (b) Qr2 dB dt (c) 1 Qr2 dB 2 dt (d) r2Q dB . dt 13. The magnetic flux through a circuit of resistance R changes by an amount  in time t . Then the total quantity of electric charge Q that during this time passes any point of the circuit is given by : (a) Q  / t (c) Q    R t (b) Q    R t (d) Q   . R 14. A uniformly wound long solenoid of inductance L and resistance R is cut into two equal parts. The two parts are then joined in parallel. Further this combination is joined to a cell of emf E. The time constant of the circuit is (a) L L 4R (b) 2R (c) 2L L R (d) R 15. A conducting disc of radius r spins about its axis with an angular x x x velocity . There is a uniform magnetic field of magnitude B per- pendicular to the plane of the disc. C is the center of the ring. (a) no emf is induced in the disc x (b) the potential difference between C and the rim is (c) C is at a higher potential than the rim (d) Current flows between C and the rim. Br2 x x x OBJECTIVE UNSOLVED LEVEL - II 1. The conductor AD moves to the right in a uniform magnetic field D directed into the paper. Mark the CORRECT option. (a) the free electrons in AD will move towards A B v (b) D will acquire a positive potential with respect to A (c) If D and A are joined by a conductor externally, a current will flow from A to D in AD (d) all the above. A 2. A square loop ABCD of edge a moves to the right with a velocity , parallel to AB. There is a uniform magnetic field of magnitude B, directed into the paper, in the region between PQ and RS only. I, II and III are three positions of the loop. [Indicate the FALSE statement] v P A B a C D Q (a) the emf induced in the loop has magnitude Bav in all three positions (b) the induced emf is zero in position II (c) the induced emf is anticlockwise in position I (d) the induced emf is clockwise in position III. 3. In figure shown, wire P1Q1 and P2Q2, both are moving towards right with speed 5 cm/sec. Resis- tance of each wire is 2  . Then current through 19  resistor is : 4 cm 19 Q1 Q2 B = 1 Tesla (a) 0 (b) 0.1 mA (c) 0.2 mA (d) 0.3 mA. C 4. A vertical conducting ring of radius R falls vertically in a horizontal magnetic field of magnitude B. The direction of B is perpendicular to the plane of the ring. When the speed of the ring is : (a) no current flows in the ring A D (b) A and D are at the same potential (c) C and E are at the same potential (d) the potential difference between A and D is BR  , with D at E a higher potential. 5. There is a uniform magnetic field B normal to the xy plane. A conductor ABC has length AB = l1, parallel to the x-axis, and length BC = l2 parallel to the y-axis. ABC moves in the xy plane with velocity x ˆi  yˆj . The potential difference between A and C is proportional to : (a) (c) xl1  yl2 xl2  yl1 (b) (d) xl2  yl1 xl1  yl2 . 6. The magnetic field perpendicular to the plane of a conducting ring of radius r changes at the rate r2 dB dB dt . (a) the emf induced in the ring is  dt (b) the emf induced in the ring is 2r2 dB dt (c) the potential difference between diametrically opposite points on the ring is half of the induced emf. (d) the emf induced in the ring is r2 . dB . dt 7. Two conducting rings of radii r and 2r move in opposite directions with velocities 2  and  respectively on a con- ducting surface S. There is a uniform magnetic field of x v 2v r 2r magnitude B perpendicular to the plane of the rings. The potential difference between the highest points of the two S rings is : (a) zero (b) 2r B (c) 4r B (d) 8r B. 8. The loop shown moves with a velocity  in a uniform magnetic L field of magnitude B, directed into the paper. The potential differ- ence between P and Q is e. (a) e  1 Bl 2 L L/2 (b) e = Bl (c) P is negative with respect to Q (d) q is positive with respect to P. 9. AB and CD are smooth parallel rails, separated by a dis- C tance L, and inclined to the horizontal at an angle  . A uni- form magnetic field of magnitude B0 , directed vertically up- L wards, exists in the region. EF is a conductor of mass m,  carrying a current i. For EF to be in equilibrium, A B0F D B E (a) i must flow from F to E (b) B0 il = m gtan  (c) B0 il = m gsin  (d) B0 il = mg. 10. A particle with charge +Q and mass m enters a magnetic field of Y magnitude B, existing only to the right of the boundary YZ. The x B direction of the motion of the particle is perpendicular to the direc- m tion of B. Let field will be : T  2 QB . The time spend by the particle in the x (a) T (b) 2T Z (c) T   2  (d) T   2  .  2   2      11. In the figure the magnet is moved along the axis of coil from one position to another position in 103 sec. Now magnet is at rest for 2 sec, in its new position. The duration of induced emf in the coil is : Coil (a) 103 sec (b) 2 sec (c) 2 × 103 sec (d) 0.5 × 103 sec. 12. A closed circuit consists of a source of emf E and an inductor coil of inductance L connected in series. The active resistance of whole circuit is R. At the moment t = 0 the inductance of coil abruptly L decreased to n . Then the current in the circuit immediately after that moment is : E (a) 0 (b) R nE E (c) R (d) nR . 13. A solenoid of inductance L and resistance r is connected in parallel to a resistance R and a battery of emf E. Initially the switch is closed for long time and and at t = 0, switch S is opened. Then, L, r (a) current through solenoid at any time t, after opening the switch is E(R  r) (Rr) t e L r (b) induced emf across solenoid at time t = 0 is r E2L (c) amount of heat generated in solenoid is 2r(r  R) (d) potential difference across solenoid at t = 0 is E. 14. A small, flat coil of resistance r is placed at the center of a large, closed coil of resistance R. The coils are coplanar. Their mutual inductance is M. Initially, a constant current i was flowing in the inner coil. If this current is suddenly switched off, what charge will circulate in the other coil ? (a) Mir / R2 (b) MiR / r2 (c) Mi / R (d) Mi / r. 15. A pair of parallel conducting rails lie at right angle to a uniform magnetic field of 2.0 T as shown in the figure. Two resistors 10  and 5  are to slide without friction along the rail. The distance between the conducting rails is 0.1 m. Then (a) induced current  1 150 A directed clockwise if 10  resistor is pulled to the right with speed 0.5 ms1 and 5  resistor is held fixed (b) induced current  1 300 A directed anticlockwise if 10  resistor is pulled to the right with speed 0.5 ms1 and 5  resistor is held fixed (c) induced current  1 300 A directed clockwise if 5  resistor is pulled to the left at 0.5 ms1 and 10  resistor is held at rest (d) induced current  1 150 A directed anticlockwise if 5  resistor is pulled to the left at 0.5 ms1 and 10  resistor is held at rest.