Electromagnetic Induction PYQs Set 2 (PDF)

Set 2 of 11 · Questions 31-60 of 319

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Mere Teacher · Previous Year Questions JEE Main Physics · Electromagnetic Induction · Set 2 (Q31-60)
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31. $There are two long co-axial solenoids of same length l . The inner and outer coils have radii r_{1} and r_{2} and number of turns per unit length n_{1} and n_{2} respectively. The rate of mutual inductance to the self-inductance of the inner-coil is:$ (1) $\frac{n _{1}}{n _{2}}$ (2) $\frac{n _{2}}{n _{1}} ∙ \frac{r _{1}}{r _{2}}$ (3) $\frac{n _{2}}{n _{1}} ∙ \frac{r _{1}^{2}}{r _{2}^{2}}$ (4) $\frac{n _{2}}{n _{1}}$ 32. $A current of 2.5 A flows through a coil of inductance 5 H. ne magnetic flux linked with the coil is$ (1) $0.5 Wb$ (2) $12.5 Wb$ (3) $zero$ (4) $2 Wb$ 33. $The magnetic flux through a circuit of resistance R changes by an amount Δ ϕ in a time Δ t . Then the total quantity of electric charge Q that passes any point in the circuit during the time Δ t is represented by$ (1) $Q = \frac{1}{R} \cdot \frac{Δ φ}{Δ t}$ (2) $Q = \frac{Δ φ}{R}$ (3) $Q = \frac{Δ φ}{Δ t}$ (4) $Q = R \cdot \frac{Δ φ}{Δ t}$ 34. $A long solenoid of diameter 0.1 m has 2 \times 10^{4} turns per metre. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 π^{2} Ω, the total charge flowing through the coil during this time is [NEET 2017]$ (1) $32 π μC$ (2) $16 μC$ (3) $32 μC$ (4) $16 π μC$ 35. $A metallic conductor of length 1m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad/s. If the horizontal component of earth's magnetic field is 0.2 x 1 0^{- 4} T, then emf induced between the two ends of the conductor is:$ (1) $5 μ V$ (2) $50 μ V$ (3) $5mV$ (4) $50mV$ 36. $In an ac generator, if coil of N turns and area A is rotated at v revolutions per second in a uniform magnetic field B, then the motional emf produced is equal to (At t = 0 s, the coil is perpendicular to the field)$ (1) $NBA (2 πv) sin (2 πvt)$ (2) $NBA^{2} (2 πv) sin (2 πvt)$ (3) $N^{2} B^{2} A^{2} (2 πv) sin (2 πvt)$ (4) $NBA (4 πv) sin (2 πvt)$ 37. $Consider I_{1} and I_{2} are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L_{1} = self inductance of coil 1, M_{12} = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be Options$ (1) $ϵ_{1} = - L_{1} \frac{dI _{2}}{dt} - M_{12} \frac{dI _{1}}{dt}$ (2) $ϵ_{1} = - L_{1} \frac{dI _{1}}{dt} - M_{12} \frac{dI _{2}}{dt}$ (3) $ϵ_{1} = - L_{1} \frac{d I _{1}}{dt} - M_{12} \frac{d I _{1}}{dt}$ (4) $ϵ_{1} = - L_{1} \frac{d I _{1}}{dt} + M_{12} \frac{d I _{2}}{dt}$ 38. $A long solenoid has 1000 turns. When a current of 4A flows through it, the magnetic flux linked with each turn of the solenoid is 4 \times 10^{- 3} Wb . The self-inductance of the solenoid is [NEET 2016]$ (1) $3 H$ (2) $2 H$ (3) $1 H$ (4) $4 H$ 39. $Two identical circular coils A and B are kept on a horizontal tube side by side without touching each other. If the current in the coil A increases with time, in response, the coil B$ (1) $is attracted by A$ (2) $remains stationary$ (3) $is repelled$ (4) $rotates.$ 40. $The current in self inductance L = 40 mH is to be increased uniformly from 1 amp to 11 amp in 4 milliseconds. The e.m.f. induced in inductor during process is$ (1) $100 volt$ (2) $0.4 volt$ (3) $4.0 volt$ (4) $440 volt$ 41. $A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth's magnetic field B_{H} = 3 \times 10^{- 5} T . The emf induced in the rod at an instant t = 2 s after it is released is [Take g = 10 m s^{- 2}]$ (1) $6 \times 10^{- 4} V$ (2) $3 \times 10^{- 3} V$ (3) $3 \times 10^{- 4} V$ (4) $6 \times 10^{- 3} V$ 42. $The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:$ (1) $L$ (2) $L²$ (3) $1/L²$ (4) $1/L$ 43. $A circular disc of radius 0.2 meter is placed in a uniform magnetic field of induction \frac{1}{π} (\frac{Wb}{m ^{2}}) in such a way that its axis makes an angle of 6 0^{o} with B . The magnetic flux linked with the disc is$ (1) $0.08 Wb$ (2) $0.01 Wb$ (3) $0.02 Wb$ (4) $0.06 Wb$ 44. $In a circuit L, C and R are connected in series with an alternating voltage source of frequency f . The current leads the voltage by 4 5^{o} . The value of C is$ (1) $\frac{1}{πf ( 2 πfL - R )}$ (2) $\frac{1}{2 πf ( 2 πfL - R )}$ (3) $\frac{1}{πf ( 2 πfL + R )}$ (4) $\frac{1}{2 πf ( 2 πfL + R )}$ 45. $A long solenoid has 1500 turns. When a current of 3.5 A flows through it, the magnetic flux linked with each turn of solenoid is 2.8 \times 10^{- 3} weber. The self-inductance of solenoid is$ (1) $1.2 H$ (2) $2.4 H$ (3) $3.6 H$ (4) $6 H$ 46. $In an A.C. circuit, the current flowing is I = 5 sin (100 t - π /2) ampere and the potential difference is V = 200 sin (100 t) volts. The power consumption is equal to$ (1) $20 W$ (2) $0 W$ (3) $1000 W$ (4) $40 W$ 47. $A coil having n turns and resistance RΩ is connected with a galvanometer of resistance 4 RΩ . This combination is moved in time t seconds from a magnetic flux φ_{1} Weber to φ_{2} Weber. The induced current in the circuit is$ (1) $\frac{φ _{2} - φ _{1}}{5 Rnt}$ (2) $- \frac{n ( φ _{2} - φ _{1} )}{5 Rt}$ (3) $- \frac{( φ _{2} - φ _{1} )}{Rnt}$ (4) $- \frac{n ( φ _{2} - φ _{1} )}{Rt}$ 48. $Two conducting circular loops of radii R_{1} and R_{2} are placed in the same plane with their centres coinciding. If R_{1} ≫ R_{2}, the mutual inductance M between them will be directly proportional to [NEET 2021]$ (1) $\frac{R _{1}}{R _{2}}$ (2) $\frac{R _{2}}{R _{1}}$ (3) $\frac{R _{1}^{2}}{R _{2}}$ (4) $\frac{R _{2}^{2}}{R _{1}}$ 49. $A 220-volt input is supplied to a transformer. The output circuit draws a current of 2.0 ampere at 440 volts. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is$ (1) $3.6 ampere$ (2) $2.8 ampere$ (3) $2.5 ampere$ (4) $5.0 ampere$ 50. $In which of the following devices, the eddy current effect is not used? [NEET 2019]$ (1) $Magnetic braking in train$ (2) $Electromagnet$ (3) $Electric heater$ (4) $Induction furnace$ 51. $The total emf induced in a closely would coil of N turns in which the magnetic flux linked with the coil changing at the rate \frac{d φ _{B}}{dt} is$ (1) $- N \frac{d φ _{B}}{dt}$ (2) $N \frac{d φ _{B}}{dt}$ (3) $- N \frac{d ^{2} φ _{B}}{dt ^{2}}$ (4) $- \frac{d φ _{B}}{dt}$ 52. $Two similar circular loops carry equal currents in the same direction. On moving the coils further apart, the electric current will$ (1) $remain unaltered$ (2) $increases in one and decreases in the second$ (3) $increase in both$ (4) $decrease in both$ 53. $The magnitude of the induced emf in a coil of inductance 30 mH in which the current changes from 6 A to 2 A in 2 s is$ (1) $0.06 V$ (2) $0.6 V$ (3) $1.06 V$ (4) $6 V$ 54. $The current in a coil changes from 2 A to 5 A in 0.3 s . The magnitude of emf induced in the coil is 1.0 V . The value of self-inductance of the coil is$ (1) $1.0 mH$ (2) $100 mH$ (3) $0.1 mH$ (4) $10 mH$ 55. $A wire loop of area 0.2 m^{2} has a resistance of 20Ω . A magnetic field pointing normal to the loop has a magnitude of 0.25 T and is reduced to zero at a uniform rate in 10^{- 4} sec . What is induced emf and resulting current?$ (1) $50 V, 2.5 A$ (2) $500 V, 25 A$ (3) $250 V, 12.5 A$ (4) $500 V, 2.5 A$ 56. $A boat is moving due east in a region where the earth's magnetic field is 5.0 \times 1 0^{-5} N A^{-1} m^{-1} due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 m s^{-1}, the magnitude of the induced emf in the wire of aerial is:$ (1) $1 mV$ (2) $0.75 mV$ (3) $0.50 mV$ (4) $0.15 mV$ 57. $A coil has an inductance of 2 H and resistance of 4 Ω . A 10 V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be_____x 10-2 J$ 58. $A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field 0.60 \times 10^{- 4} Wbm^{- 2} . The instantaneous value of emf induced in the wire when its velocity is 10 ms^{- 1} is____\times 10^{- 3} V$ 59. $The magnetic flux φ (in weber) linked with a closed circuit of resistance 8Ω varies with time (in seconds) as φ = 5 t^{2} - 36 t + 1 . The induced current in the circuit at t = 2 s is _____A.$ 60. $The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is \frac{x}{10} \frac{μ _{0} c}{π} \frac{V}{m} . Theefficiency of the bulb is 10% and it is a point source. The value of x is:$