Electromagnetic Induction PYQs Set 9 (PDF)

Set 9 of 11 · Questions 241-270 of 319

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Mere Teacher · Previous Year Questions JEE Main Physics · Electromagnetic Induction · Set 9 (Q241-270)
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241. $A long solenoid of radius R carries a time dependent current I = I_{0} t (1 - t) . A ring of radius 2 R is placed coaxially near its centre. During the time interval 0 \leq t \leq 1, the induced current I_{R} and the induced emf V_{R} in the ring vary as:$ (1) $current will change its direction and its emf will be zero at t = 0.25 sec$ (2) $current will not change its direction & emf will be maximum at t = 0.5 sec$ (3) $current will not change direction and emf will be zero at 0.25 sec .$ (4) $At t = 0.5 direction of I_{R} reverses and V_{R} is zero$ 242. $The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of 1 cms^{- 1} . At some instant, a part of L is in a uniform magnetic field of 1T, perpendicular to the plane of the loop. If the resistance of L is 1.7Ω, the current in the loop at that instant will be close to:$ (1) $60 μA$ (2) $170 μA$ (3) $150 μA$ (4) $115 μA$ 243. $An aeroplane, with its wings spread 10m, is flying at a speed of 180km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 \times 10^{- 4} Wb / m^{2} and the angle of dip is 60°. The emf induced between the tips of the plane wings will be?$ (1) $88.37 mV$ (2) $62.50m V$ (3) $54.125 mV$ (4) $108.25 mV$ 244. $A copper wire is wound on a wooden frame, whose shape is that of a square if each side of the frame is increased by a factor of 3 , keeping the number of turns of the coil per unit length of the frame the same, then the self-inductance of the coil:$ (1) $increases by a factor of 3$ (2) $decreases by a factor of 93$ (3) $increases by a factor of 27$ (4) $decreases by a factor of 9$ 245. $As shown in the figure, a battery of emf ϵ is connected to an inductor L and resistance R in series. The switch is closed at t = 0 . The total charge that flows from the battery, between t = 0 and t = t_{c} (t_{c} is the time constant of the circuit) is$ (1) $\frac{ϵ L}{R ^{2} e}$ (2) $\frac{ϵ L}{R ^{2}}$ (3) $\frac{ϵ L ( 1 - \frac{1}{e} )}{R}$ (4) $\frac{ϵ L}{R}$ 246. $An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x -axis with angular frequency ω, the average power loss in the loop due to Joule heating is$ (1) $\frac{πabBω}{R}$ (2) $\frac{π ^{2} a ^{2} b ^{2} B ^{2} ω ^{2}}{2 R}$ (3) $Zero$ (4) $\frac{π ^{2} a ^{2} b ^{2} B ^{2} ω ^{2}}{R}$ 247. $At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is:$ (1) $56 μV$ (2) $28 μV$ (3) $30 μV$ (4) $48 μV$ 248. $An inductor of inductance L = 400 mH and resistors of resistances R_{1} = 2 Ω and R_{2} = 2 Ω are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is:$ (1) $\frac{12}{t} e^{- 3 t} V$ (2) $6 (1 - e^{- t /0.2}) V$ (3) $12 e^{-5 t} V$ (4) $6 e^{-5 t} V$ 249. $In the above figure, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively are through the directions [NEET 2024]$ (1) $AB and DC$ (2) $BA and CD$ (3) $AB and CD$ (4) $BA and DC$ 250. $In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly point 'C' is disconnected from point 'A' and connected to point 'B' at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to:$ (1) $\frac{e}{1 - e}$ (2) $1$ (3) $-1$ (4) $\frac{1 - e}{e}$ 251. $A series R‐C circuit is connected to an alternating voltage source. Consider two situations: (i) When capacitor is air filled. (ii) When capacitor is mica filled. Current through resistor is i and voltage across capacitor is V then$ (1) $i_{a} = i_{b}$ (2) $V_{a} = V_{b}$ (3) $V_{a} < V_{b}$ (4) $V_{a} > V_{b}$ 252. $A beam of light travelling along X-axis is described by the electric field E_{y} = 900 sin ω (t-x/c). The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of 3 x 107 ms-1 will be: [Given speed of light = 3 x 108 ms-1]$ (1) $1 : 1$ (2) $1 : 10$ (3) $10 : 1$ (4) $l : 2$ 253. $A square loop of side 15 cm being moved towards right at a constant speed of 2 cm / s as shown in figure. The front edge enters the 50 cm wide magnetic field at t = 0 . The value of induced emf in the loop at t = 10 s will be:$ (1) $0.3 mV$ (2) $zero$ (3) $4.5 mV$ (4) $3 mV$ 254. $Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and t = \frac{L}{R} is:$ (1) $\frac{2.7 EL}{R ^{2}}$ (2) $\frac{EL}{2.7 R ^{2}}$ (3) $\frac{7.3 EL}{R ^{2}}$ (4) $\frac{EL}{7.3 R ^{2}}$ 255. $An aircraft with a wingspan of 40 m flies with a speed of 1080 km / hr in the eastward direction at a constant altitude in the northern hemisphere, where the vertical component of the earth's magnetic field 1.75 \times 10^{- 5} T . Then the emf developed between the tips of the wings is$ (1) $0.34 V$ (2) $2.1 V$ (3) $0.5 V$ (4) $0.21 V$ 256. $The magnetic flux through the triangular loop shown in the figure below: where a uniform magnetic field of strength 2 T points perpendicularly into the plane of the triangle.$ (1) $10^{- 4} Wb$ (2) $2\times 1 0^{- 4} Wb$ (3) $1 Wb$ (4) $2 Wb$ 257. $A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is$ (1) $four times per revolution$ (2) $six times per revolution$ (3) $once per revolution$ (4) $twice per revolution$ 258. $A coil of self-inductance 10 mH and resistance 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω. After the switch is closed, the time taken for the current to attain 80% of the saturation value is: [Take ln 5 = 1.6]$ (1) $0.324 s$ (2) $0.103 s$ (3) $0.002 s$ (4) $0.016 s$ 259. $A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf (ϵ) with time (t) is given by$ (1) (2) (3) (4) 260. $The current i in a coil varies with time as shown in the figure. The variation of induced emf with time would be$ (1) (2) (3) (4) 261. $A bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a net acceleration$ (1) $= g$ (2) $Zero$ (3) $< g$ (4) $> g$ 262. $In a coil of resistance10 Ω, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is$ (1) $8$ (2) $2$ (3) $6$ (4) $4$ 263. $A small square loop of wire of side l is placed inside a large square loop of wire L (L >> I). Both loops are coplanar and their centers coincide at point O as shown in figure. The mutual inductance of the system is:$ (1) $\frac{2 2 μ _{0} L ^{2}}{πl}$ (2) $\frac{μ _{0} l ^{2}}{2 2 πL}$ (3) $\frac{2 2 μ _{0} l ^{2}}{πL}$ (4) $\frac{μ _{0} L ^{2}}{2 2 πl}$ 264. $Two conducting circular loops A and B are placed in the same plane with their centers coincidng as shown in figure. The mutual inductance between them is:$ (1) $\frac{μ _{0} π b ^{2}}{2 a}$ (2) $\frac{μ _{o}}{2 π} \cdot \frac{b ^{2}}{a}$ (3) $\frac{μ _{0}}{2 π} \cdot \frac{a ^{2}}{b}$ (4) $\frac{μ _{0} π a ^{2}}{2 b}$ 265. $The r.m.s. value of potential difference V shown in the figure is$ (1) $\frac{V _{0}}{3}$ (2) $V_{0}$ (3) $\frac{V _{0}}{2}$ (4) $\frac{V _{0}}{2}$ 266. $A metallic cube of side 15 cm moving along y-axis at a uniform velocity of 2 m s^{- 1} . In a region of uniform magnetic field of magnitude 0.5T directed along z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be mV.$ 267. $When a coil is connected across a 20 V dc supply, it draws a current of 5 A . When it is connected across 20 V, 50 Hz ac supply, it draws a current of 4 A . The self inductance of the coil is_____mH . (Take π = 3)$ 268. $As per the given figure, if \frac{dI}{dt} = -1 A/s then the value of V_{A B} at this instant will be_____V.$ 269. $A square loop of side 10 cm and resistance 0.7Ω is placed vertically in east-west plane. A uniform magnetic field of 0.20 T is set up across the plane in north east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, magnitude of induced emf is x \times 10^{- 3} V . The value of x is$ 270. $A rod of length 60 cm rotates with a uniform angular velocity 20 rads^{- 1} about its perpendicular bisector, in a uniform magnetic filed 0.5 T . The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is_____V.$