Electromagnetic Induction PYQs Set 10 (PDF)

Set 10 of 11 · Questions 271-300 of 319

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Mere Teacher · Previous Year Questions JEE Main Physics · Electromagnetic Induction · Set 10 (Q271-300)
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271. $A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic field B about an axis perpendicular to B . Magnetic flux ϕ and induced emf ϵ across it, at an instant when B is parallel to the plane of coil, are:$ (1) $ϕ = AB, ϵ = 0$ (2) $ϕ = 0, ϵ = 0$ (3) $ϕ = 0, ϵ = NABω$ (4) $ϕ = AB, ϵ = NABω$ 272. $A long straight solenoid with cross-sectional radius a and number of turns per unit length n has a current varying with time as I (As^{- 1}) . The magnitude of the electric field as a function of distance r from the solenoid axis is$ (1) $\frac{n μ _{0} a ^{2} l}{2 r}$ (2) $\frac{μ _{0} ln}{2 a}$ (3) $\frac{n a ^{2} l}{2 μ _{0} r}$ (4) $\frac{μ _{0} la}{2 n}$ 273. $The current flowing through an inductance coil of self inductance 6 mH at different time instants is as shown. The emf induced between t = 20 s and t = 40 s is nearly$ (1) $2 \times 10^{- 2} V$ (2) $3 \times 10^{- 4} V$ (3) $4 \times 10^{- 3} V$ (4) $30 \times 10^{2} V$ 274. $A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is:$ (1) $\frac{2 B ω l ^{2}}{2}$ (2) $\frac{3 B ω l ^{2}}{2}$ (3) $\frac{4 B ω l ^{2}}{2}$ (4) $\frac{5 B ω l ^{2}}{2}$ 275. $In a coil resistance 100Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:$ (1) $275 Wb$ (2) $200 Wb$ (3) $225 Wb$ (4) $250 Wb$ 276. $A thin semicircular conducting ring (PQR) of radius 'r' is falling with its plane vertical in a horizontal magnetic field B, as shown in figure. The potential difference developed across the ring when its speed is v, is:$ (1) $Zero$ (2) $B v π r^{2} /2 and P is at higher potential$ (3) $πrBv and R is at higher potential$ (4) $2rBv and R is at higher potential$ 277. $A cooper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil?$ (1) $Decrease by a factor of 9$ (2) $Increase by a factor of 27$ (3) $Decrease by a factor of 3$ (4) $Increases by a factor of 93$ 278. $A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is$ (1) $\frac{2}{ln 2}$ (2) $\frac{1}{2} ln 2$ (3) $2 ln 2$ (4) $ln 2$ 279. $A uniform magnetic field is restricted within a region of radius r . Ihe magnetic field changes with time at a rate \frac{d B}{dt} . Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e . m . f . generated is$ (1) $zero in loop 1 and zero in loop 2$ (2) $- \frac{d B}{dt} π r^{2} in loop 1 and - \frac{d B}{dt} π r^{2} in loop 2$ (3) $zero in loop 1 and - \frac{d B}{dt} π r^{2} in loop 2$ (4) $- \frac{d B}{dt} π r^{2} in loop 1 and zero in loop 2$ 280. $In the circuit shown below, the key K is closed at t = 0. The current through the battery is:$ (1) $\frac{V R _{1} R _{2}}{R _{1}^{2} + R _{2}^{2}} at t = 0 and \frac{V}{R _{2}} at t = ¥$ (2) $\frac{V}{R _{2}} at t = 0 and \frac{V ( R _{1} + R _{2} )}{R _{1} R _{2}} at t = ¥$ (3) $\frac{V}{R _{2}} at t = 0 and \frac{V R _{1} R _{2}}{R _{1}^{2} + R _{2}^{2}} at t = ¥$ (4) $\frac{V ( R _{1} + R _{2} )}{R _{1} R _{2}} at t = 0 and \frac{V}{R _{2}} at t = ¥$ 281. $Figure shows the circuit that contains three resistances (9Ω each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is____A.$ (1) $2$ (2) $1$ (3) $zero$ (4) $3$ 282. $When the key K is pressed at time t = 0, then which of the following statement about the current I in the resistor AB ofthe given circuit is true?$ (1) $I oscillates between 1 mA and 2 mA$ (2) $at t = 0, I = 2 mA and with time it goes to 1 mA$ (3) $I = 1 mA at all t$ (4) $I = 2 mA at all t .$ 283. $A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The center of the small loop is on the axis of the bigger loop. The distance between their centers is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is:$ (1) $9.1 \times 1 0^{-11} weber$ (2) $6 \times 1 0^{-11} weber$ (3) $3.3 \times 1 0^{-11} weber$ (4) $6.6 \times 1 0^{-9} weber$ 284. $In an a . c . circuit the e.m.f. (ϵ) and the current (i) at any instant are given respectively by e = E_{0} sin ω t, i = I_{0} sin (ωt - φ) The average power in the circuit over one cycle of a . c . is$ (1) $\frac{E _{0} I _{0}}{2} cos ϕ$ (2) $E_{0} I_{0}$ (3) $\frac{E _{0} I _{0}}{2}$ (4) $\frac{E _{0} I _{0}}{2} sin ϕ$ 285. $Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I = 10 sin (ωt) A, where ω = 1000 rad . /s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed v = 1 cm / s . The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is α / 2 μ A . The value of α is____. [Resistance of the loop = 10Ω]$ (1) $197$ (2) $80$ (3) $100$ (4) $280$ 286. $Eddy currents are produced when$ (1) $a metal is kept in varying magnetic field$ (2) $a metal is kept in steady magnetic field$ (3) $a circular coil is placed in a magnetic field$ (4) $through a circular coil, current is passed$ 287. $Given below are two statements: Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $Both Statement I and Statement II are correct.$ (2) $Both Statement I and Statement II are incorrect.$ (3) $Statement I is correct but Statement II is incorrect.$ (4) $Statement I is incorrect but Statement II is correct.$ 288. $The time constant of C‐R circuit is$ (1) $1/ CR$ (2) $C / R$ (3) $CR$ (4) $R / C$ 289. $The induced emf cannot be produced by$ (1) $moving a magnet near a circuit$ (2) $moving a circuit near a magnet$ (3) $changing the current in one circuit placed near the other$ (4) $maintaining large but constant current in a circuit$ 290. $A wheel with 10 spokes each of length L m is rotated with a uniform angular velocity (ω) in a plane normal to the magnetic field B . The emf induced between the axle and the rim of the wheel$ (1) $\frac{1}{2} N ω B L^{2}$ (2) $\frac{1}{2} ω B L^{2}$ (3) $ω b L^{2}$ (4) $N ω B L^{2}$ 291. $Figure shows a circuit that contains three identical resistors with resistance R = 9.0Ω each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf ϵ = 18 V ne current i through the batteryjust after the switch closed is$ (1) $0.2 A$ (2) $2 A$ (3) $4 A$ (4) $2 mA$ 292. $A metallic rod of length 'L' is rotated with an angular speed of ' ω' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be:$ (1) $\frac{1}{4} B^{2} Lω$ (2) $\frac{1}{4} B L^{2} ω$ (3) $\frac{1}{2} B L^{2} ω$ 293. $A rectangular loop of wire is placed in the XY -plane with its side of length 3 cm parallel to the X -axis and the side of length 4 cm parallel to the Y -axis. It is moving in the positive X -direction with the speed 10 cm / s . A magnetic field exists in the space with its direction parallel to the Z -axis. The field decreases by 2 \times 10^{- 3} T / cm along the positive X -axis and increases in time by 2 \times 10^{- 2} T / s . The induced emf in the wire is$ (1) $-4.8\times 1 0^{- 5} V$ (2) $4.8 \times 10^{- 5} V$ (3) $0$ (4) $3.6 \times 10^{- 5} V$ 294. $The magnitude of induced emf is directly proportional to the rate of change of magnetic flux linked with the coil. This statement is known as$ (1) $Ohm's law$ (2) $Lenz's law$ (3) $Faraday's law$ (4) $Ampere's law$ 295. $X PQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is l . A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L > l) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is m / s . (g = acceleration due to gravity)$ (1) $\frac{8 mgR}{B ^{2} l ^{2}}$ (2) $\frac{2 mgR}{B ^{2} L ^{2}}$ (3) $\frac{mgR}{B ^{2} l ^{2}}$ (4) $\frac{2 mgR}{B ^{2} l ^{2}}$ 296. $A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of 10^{2} As^{- 1} . The value of the potential difference V_{P} - V_{Q}, (in volts) at that instant, is \dots \dots \dots \dots .$ 297. $A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E \propto t^{n}, then value of n is .$ 298. $An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area 24 c m^{2} . The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12 Ω . If an externally applied uniform magnetic field in the core along its axis changes from 1. 5 T in one direction to 1. 5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be_____mC.$ 299. $A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of 60^{\circ} with vertical, then maximum induced EMF between the point of suspension and point of oscillation is____mV. (Take g = 10 m / s^{2})$ 300. $A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5 Ω, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m s^{- 1} will be_______\times 1 0^{- 3} N.$