Electromagnetic Induction PYQs Set 8 (PDF)

Set 8 of 11 · Questions 211-240 of 319

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Mere Teacher · Previous Year Questions JEE Main Physics · Electromagnetic Induction · Set 8 (Q211-240)
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211. $A circular coil of area 100 cm^{2} and 20 turns is kept in magnetic field of flux density 2 Wb - m^{2} . It rotates from a position where its plane makes an angle of 30^{\circ} with the field to a position perpendicular to the field in a time 0.2 s. Find the magnitude of the emf induced in the coil due to its rotation.$ (1) $2 V$ (2) $3 V$ (3) $1.5 V$ (4) $1 V$ 212. $A square loop of side 20cm and resistance 1Ω is moved towards right with a constant speed υ_{0} . The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4Ω . What should be the value of v_{0} so that a steady current of 2mA flows in the loop?$ (1) $1 m/s$ (2) $1cm/s$ (3) $102 m/s$ (4) $10-2 cm/s$ 213. $The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance:$ (1) $A-Flux, B-Power dissipated, C-EMF$ (2) $A-Power dissipated, B-Flux, C-EMF$ (3) $A-Flux, B-EMF, C-Power dissipated$ (4) $A-EMF, B-Power dissipated, C-Flux$ 214. $Two coils of self inductance L_{1} and L_{2} are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be:$ (1) $\frac{1}{L _{1}} + \frac{1}{L _{2}} + \frac{1}{M}$ (2) $L_{1} + L_{2} + M$ (3) $L_{1} + L_{2} + 2M$ (4) $L_{1} + L_{2} - 2M$ 215. $As shown in the figure, a battery of emf ε is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = t_{c} (t_{c} is the time constant of the circuit) is:$ (1) $\frac{ϵ L}{R ^{2}} (1 - \frac{1}{e})$ (2) $\frac{ϵ R}{e L ^{2}}$ (3) $\frac{ϵ L}{R ^{2}}$ (4) $\frac{ϵ L}{e R ^{2}}$ 216. $For the given circuit the current i through the battery when the key in closed and the steady state has been reached is .......$ (1) $6A$ (2) $25A$ (3) $10A$ (4) $0A$ 217. $Near a circular loop of conducting wire as shown in the figure an electron moves along a straight line. The direction of the induced current if any in the loop is$ (1) $variable$ (2) $clockwise$ (3) $anticlockwise$ (4) $zero.$ 218. $A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2Ω then the force needed to move the rod towards right with constant speed (v) of 1.5 m / s is____N.$ (1) $5.7 \times 10^{- 2}$ (2) $7.5 \times 10^{- 2}$ (3) $7.5 \times 10^{- 3}$ (4) $5.7 \times 10^{- 3}$ 219. $There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then$ (1) $current is induced in the loop in the anticlockwise direction$ (2) $current is induced in the loop in the clockwise direction$ (3) $AC is induced in the loop$ (4) $no current is induced in the loop.$ 220. $A L C R circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant b, the correct equivalence would be:$ (1) $L \Leftrightarrow \frac{1}{b}, C \Leftrightarrow \frac{1}{m}, R \Leftrightarrow \frac{1}{k}$ (2) $L \Leftrightarrow k, C \Leftrightarrow b, R \Leftrightarrow m$ (3) $L \Leftrightarrow m, C \Leftrightarrow \frac{1}{k}, R \Leftrightarrow b$ (4) $L \Leftrightarrow m, C \Leftrightarrow k, R \Leftrightarrow b$ 221. $A cycle wheel of radius 0.5 m is rotated with constant angular velocity of 10 rad / s in a region of magnetic field of 0.1 T which is perpendicular to the plane of the wheel. The emf generated between its center and the rim is [NEET 2019]$ (1) $0.25 V$ (2) $0.125 V$ (3) $0.5 V$ (4) $zero$ 222. $At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is:$ (1) $28 µV$ (2) $36 µV$ (3) $48 µV$ (4) $56 µV$ 223. $Two straight conducting rails form a right angle as shown below. A conducting bar in contact with the rails starts at the vertex at time t = 0 and moves with constant velocity of v = 5 m / s along them. A magnetic field with B = 0.1 T is directed out of the page. The absolute value of the emf around the triangle at the time t = 4 s will be$ (1) $10 V$ (2) $15 V$ (3) $20 V$ (4) $30 V$ 224. $A rod of length 2 m slides with a speed of 5 m s^{- 1} on a rectangular conducting frame as shown in figure. There exists a uniform magnetic field of 0.04 T perpendicular to the plane of the figure. If the resistance of the rod is 3Ω . The current through the rod is$ (1) $0.75 A$ (2) $1.33 A$ (3) $75 mA$ (4) $133 mA$ 225. $Consider a toroid with rectangular cross section, of inner radius a, outer radius b and height h, carrying n number of turns: Then the self-inductance of the toroidal coil when current I passing through the toroid is$ (1) $\frac{μ _{0} n ^{2} h}{2 π} ln (\frac{b}{a})$ (2) $\frac{μ _{0} nh}{2 π} ln (\frac{b}{a})$ (3) $\frac{μ _{0} n ^{2} h}{2 π} ln (\frac{a}{b})$ (4) $\frac{μ _{0} nh}{2 π} ln (\frac{a}{b})$ 226. $A simple pendulum with bob of mass ' m' and conducting wire of length ' L' swings under gravity through an angle ' θ'. The component of earth's magnetic field in the direction perpendicular to swing is ' B'. Maximum e.m.f. induced across the pendulum is (g = acceleration due to gravity)$ (1) $2 BLsin (\frac{θ}{2}) (gL)^{1/2}$ (2) $BLsin (\frac{θ}{2}) (gL)$ (3) $2 BLsin (\frac{θ}{2}) (gL)^{3/2}$ (4) $2 BLsin (\frac{θ}{2}) (gL)^{2}$ 227. $In the given circuit the reading of voltmeter V_{1} and V_{2} are 300 volts each. The reading of the voltmeter V_{3} and ammeter A are respectively$ (1) $150 V, 2.2 A$ (2) $220 V, 2.2 A$ (3) $220 V, 2.0 A$ (4) $100 V, 2.0 A$ 228. $A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil? Three positions shown describe : (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit.$ (1) (2) (3) (4) 229. $A square loop of side 2 cm enters a magnetic field with a constant speed of 2 cm s^{- 1} as shown. The front edge enters the field at t = 0 s . Which of the following graph will correctly depicts the induced emf in the loop? [Take clockwise direction positive]$ (1) (2) (3) (4) 230. $In the circuit given in figure, 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading will be$ (1) $zero in 1, maximum in 2$ (2) $maximum in both 1 and 2$ (3) $zero in both 1 and 2$ (4) $maximum in 1, zero in 2.$ 231. $A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. The potential difference developed across the ring when its speed is v,$ (1) $zero$ (2) $\frac{Bvπ r ^{2}}{2} and P is at higher potential$ (3) $πrBv and R is at higher potential$ (4) $2 rBv and R is at higher potential$ 232. $Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of \frac{1}{2} Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm / s, induced emf between points A and E is_________ mV.$ 233. $A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is 4 x 1 0^{- 3} T and the angle of dip is 45°. The emf induced in the rod is ______ mV$ 234. $Inductance of a coil with 10^{4} turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10Ω . The energy density in the inductor when the current reaches (\frac{1}{e}) of its maximum value is απ \times \frac{1}{e ^{2}} J / m^{3} . The value of α is____. (μ_{0} = 4 π \times 10^{- 7} Tm / A) .$ 235. $The magnetic field B crossing normally a square metallic plate of area 4 m^{2} is changing with time as shown in figure. The magnitude of induced emf in the plate during t = 2 s to t = 4 s, is_____mV.$ 236. $In the given figure, an inductor and resistor are connected in series with a battery of emf E volt. \frac{E ^{a}}{2 b} J s^{- 1} represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of \frac{b}{a} will be_____.$ 237. $In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A / s . At an instant when R is 12Ω, the value of the current in the circuit will be A.$ 238. $Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T1 is connected to T2. As the current in R = 6Ω attains a maximum value of steady state level, T1 is disconnected from T2 and immediately connected to T3. Potential drop across r = 3Ω resistor immediately after T1 is connected to T3 is ___ V. (Round off to the Nearest Integer)$ 239. $A small square loop of wire of side l is placed inside a large square loop of wire of side L (L = l^{2}) . The loops are coplanar and their centers coinside. The value of the mutual inductance of the system is x \times 10^{- 7} H, where x =_____$ 240. $A square loop PQRS having 10 turns, area 3.6 \times 10^{- 3} m^{2} and resistance 100Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is_____\times 10^{- 6} J .$