Faraday's & Lenz's Law Motional EMF — Practice Questions

Free NEET Physics multiple-choice questions on Faraday's & Lenz's Law Motional EMF. Attempt each question and reveal the answer with a full explanation.

The magnetic flux linked with a coil (in Wb) is given by the equation = 5t 2 + 3t + 16 . The magnitude of induced emf in the coil at time t = 4 s will be: 43 V 33 V 10 V 16 V A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m/s, at right angles to the horizontal component of the earth's magnetic field, 0.30 10 -4 Wb/m 2 . The instantaneous value of the emf induced in the wire is: 1.5 10 -3 V 1.1 10 -3 V 2.5 10 -3 V 1.5 10 -4 V A parallel plate capacitor with plate area A and separation d is being charged by a current i . The displacement current through a plane surface of area A/2 parallel to the plates and situated between them is: i/2 i i/4 2i A square loop of side a and resistance R is moved with a constant velocity v out of a uniform magnetic field B acting perpendicular to its plane. The work done in pulling the loop out of the field is: B 2 a 3 v / R B 2 a 2 v / R B a 2 v / R B 2 a 3 v 2 / R The magnetic flux through a stationary loop of wire with total resistance R varies as = at(T - t) where a is a constant. The total heat generated in the loop during the time interval t=0 to t=T is: a 2 T 3 / (3R) a 2 T 2 / R a 2 T 3 / R a 2 T / (3R) A parallel plate capacitor is being charged by a time-varying current. If the radius of the plates is R , the displacement current density at a distance r < R from the axis is: 1 R 2 dq dt r R 3 dq dt 1 2 r dq dt r 2 R 4 dq dt A long solenoid has a radius R and n turns per unit length. If the current through it is I = I 0 t , the magnitude of the induced electric field at a distance r < R from the axis is: 1 2 0 n r I 0 t 0 n r I 0 t 1 2 0 n R I 0 t 0 n I 0 r t A rectangular coil of 20 turns and area 25 cm 2 is placed in a uniform magnetic field of 0.10 T. If the resistance of the coil is 5 , the charge that flows through the coil when it is rotated from 0 to 90 (with respect to the field direction) is: 10 -3 C 10 -2 C 10 -4 C 10 -1 C A metallic rod of length l is tied to a string of length 2l and made to rotate with angular speed on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B , the emf induced across the ends of the rod is: 3.5 B l 2 2 B l 2 0.5 B l 2 4 B l 2 The unit of the ratio of magnetic flux to current I is equivalent to the unit of: Resistance Time Resistance / Time Voltage Time Current Time A long solenoid of radius R has n turns per unit length and carries a time-varying current I = I 0 t . The magnitude of the induced electric field at a distance r ( r > R ) from the axis of the solenoid is: 0 n I 0 R 2 t 2r 0 n I 0 r t 2 0 n I 0 R t 2 Zero A circular loop of radius a is placed in a uniform magnetic field B such that its plane is perpendicular to B . If the loop is rotated about its diameter with constant angular speed , the average power dissipated in the loop of resistance R over one cycle is: (B 2 2 a 4 2) / (2R) (B 2 2 a 4 2) / R (B a 2 ) / R Zero The magnetic flux linked with a square loop of side L in a magnetic field B is . If the side of the square is doubled and the magnetic field is halved, the new flux will be: 2 4 /2 A conducting loop of finite resistance lies on the x-y plane. There is a constant magnetic field in the z direction. The area of the loop varies with time t , as A=A 0(1+ t) in appropriate units. The figure that correctly indicates the qualitative behaviour of the power P dissipated in the loop as a function of time is: Graph (1) Graph (2) Graph (3) Graph (4) Which of the following properties of a wave is used in a hot-wire ammeter? Heating effect Magnetic effect Chemical effect None of these A conductor rod of length l is moving with velocity v in a direction perpendicular to its length and also perpendicular to a uniform magnetic field B . The potential difference induced between the two ends of the rod is: Blv 1 2 Blv Blv 2 B 2lv 2 A circular loop of radius r is placed in a region of uniform magnetic field B such that the plane of the loop is perpendicular to the magnetic field. If the loop is rotated about its diameter with an angular velocity , the maximum induced emf is: B r 2 2 B r 2 B r 2 / 2 Zero A coil of resistance 400 is placed in a magnetic field. If the magnetic flux (Wb) linked with the coil varies with time t (s) as = 50t 2 + 4 . The current in the coil at t = 2 s is: 0.5 A 0.1 A 2.0 A 1.0 A A coil of 100 turns and area 5 cm 2 is placed in a magnetic field of 0.2 T. The normal to the plane of the coil makes an angle of 60 with the direction of the magnetic field. The magnetic flux linked with the coil is: 5 10 -3 Wb 1 10 -2 Wb 8.66 10 -3 Wb 5 10 -4 Wb The magnetic energy density u B (energy per unit volume) in a region of free space with a magnetic field B is given by: B 2 2 0 B 2 0 2 0 B 2 2 B 2 2 0 2 A square loop of side a is moving with constant velocity v out of a uniform magnetic field B perpendicular to its plane. The induced emf in the loop is constant until: The loop is entirely out of the field The loop is entirely inside the field The loop starts entering the field The velocity becomes zero In a region of magnetic field B , a loop of area A is placed. The angle between the magnetic field and the normal to the area is . If the magnetic field changes to B/2 and the area is doubled, what is the new flux linked with the loop? BA 2 BA 0.5 BA BA The coefficient of mutual inductance between two coils is 2.5 H. If the current in the primary coil changes from 0 to 20 A in 0.1 s, the induced emf in the secondary coil is: 500 V 200 V 50 V 100 V The displacement current flows in the region between the plates of a capacitor when the charge on the capacitor is: Changing with time Constant Zero Infinite Which of the following quantity has the same unit as that of time? L / R 1 / LC RL C / L A conductor of length 0.4 m is moving with a speed of 7 m/s perpendicular to a magnetic field of intensity 0.9 Wb/m 2 . The induced emf across the conductor is: 2.52 V 1.26 V 5.04 V 25.2 V The unit of induced electric field is: V/m V Wb N/C s Lenz's law is a consequence of the law of conservation of: Energy Charge Mass Momentum Which of the following equations represents Faraday's Law in its general integral form? E dl = - d B dt B dl = 0 I E dA = Q/ 0 B dA = 0 A hot-wire ammeter reads 10 A in an AC circuit. The peak value of the current is: 10 2 A 10 / 2 A 10 A 20 / A A conductor of length l rotates with angular velocity in a plane perpendicular to a uniform magnetic field B . The induced emf between its center and one of its ends is: 1 2 B l 2 B l 2 1 2 B 2 l Zero Dimensions of the physical quantity 1/ 0 0 are: [LT -1 ] [L -1 T] [L 2T -2 ] [ML 2T -2 A -2 ] As a result of change in the magnetic flux linked to the closed loop shown in the figure, an e.m.f. V volt is induced in the loop. The work done (joules) in taking a charge Q coulomb once along the loop is- QV QV/2 2QV Zero The magnetic flux linked with a coil is given by = 8t 2 + 3t + 5 . The magnitude of the induced emf at t = 2 s is: 35 V 19 V 32 V 40 V The core of a transformer is laminated because:- Energy losses due to eddy currents may be minimised The weight of the transformer may be reduced Rusting of the core may be prevented Ratio of voltage in primary and secondary may be increased Two coils of self inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:- 10 mH 6mH 4 mH 16 mH The primary and secondary coil of a transformer have 50 and 1500 turns respectively. If the magnetic flux linked with the primary coil is given by = 0 + 4t , where is in webers, t is time in seconds and 0 is a constant, the output voltage across the secondary coil is 120 volts 220 volts 30 volts 90 volts A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5 amp, the efficiency of the transformer is approximately 50% 90% 10% 30%. A conducting circular loop is placed in a uniform magnetic field 0.04T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is : 1.6 v 3.2 v 4.8 v 0.8 v A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is Once per revolution Twice per revolution Four times per revolution Six times per revolution 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 10 -3 Wb. The self inductance of the solenoid is :- 4H 3H 2H 1H The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance 1.389 H 138.88 H 0.138 H 13.89 H In which of the following devices, the eddy current effect is not used? Electric heater Induction furnace Magnetic braking in train Electromagnet A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is 0.5 weber 1 weber Zero weber 2 weber If the current I through an inductor L varies with time t as I = kt 2 , where k is a constant, the variation of induced emf magnitude |e| with time is represented by: A straight line passing through the origin A parabola opening upwards A straight line with a non-zero intercept A rectangular hyperbola The magnetic energy stored in an inductor of inductance 4 H carrying a current of 2 A is 4 J 4 mJ 8 mJ 8 J A rectangular wire loop of sides 8 cm and 3 cm with a small cut, is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is 2 cm s -1 , in a direction normal to the shorter side of the loop, will be : 1.8 10 -4 volt 1.3 10 -4 volt 1.2 10 -4 volt 4.8 10 -4 volt A circular wheel with 10 metal spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of earth's magnetic field B H at a place. If B H = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? ( 1 G = 10 -4 T) 6.28 10 -5 V 3.14 10 -5 V 1.25 10 -4 V 2.51 10 -4 V A 0.1 m long conducting rod AB moves with a speed of 10 m/s perpendicular to a magnetic field of 0.5 T. The ends of the rod are connected to a 10 resistance. The heat generated in the resistance in 1 minute is: 1.5 mJ 0.5 mJ 2.5 mJ 3.0 mJ The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux linked with the primary coil is given by = 0 + 4t , where is in webers, t is in seconds and 0 is a constant, the output voltage across the secondary coil is: 120 V 90 V 60 V 30 V In a coil of resistance 10 , 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: 2 8 6 4 In a coil of resistance 10 , the magnetic flux linked with the coil varies with time as = 6t 2 - 5t + 1 . What is the magnitude of the induced charge that flows through the coil from t = 0 to t = 0.25 s? 0.125 C 0.25 C 0.5 C 0.01 C A magnet is moved towards a coil, first quickly and then slowly. In which case is the induced emf and induced charge more? Emf is more in the first case, charge is same in both Emf is more in the first case, charge is more in the first case Emf is same in both, charge is more in the first case Emf and charge are same in both cases A circular coil of radius R is rotating in a uniform magnetic field B with angular velocity . The maximum emf induced in the coil is: B R 2 2 B R 2 B R 2 1 2 B R 2 A metal rod of length L rotates with an angular frequency about an axis passing through one end and perpendicular to its length, in a uniform magnetic field B . The induced emf between the ends of the rod is: 1 2 B L 2 B L 2 2 B L 2 1 4 B L 2 The magnetic flux linked with a coil varies with time as = 4t 2 + 2t + 1 (Wb). The induced current in the coil at t = 1 s, if the resistance is 10 , is: 1.0 A 0.5 A 0.4 A 10 A A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is: Less than g Equal to g More than g Zero The figure shows a circular loop of radius r and a long straight wire carrying a current i . The loop is moving with a velocity v away from the wire. The induced emf in the loop at the instant shown is: Directed clockwise Directed anti-clockwise Zero Directed out of the page A copper disc of radius 0.1 m rotated about its centre with 10 rev/s in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is: 10 -2 V 10 -2 V 2 10 -2 V 10 -1 V 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 passes any point in the circuit during the time t is represented by: Q = / R Q = / t Q = R / t Q = / (R t) A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth's magnetic field at the location has a magnitude of 5 10 -4 T and the dip angle is 30 ? 3.125 V 0.125 V 31.25 V 312.5 V A conducting rod of length l is rotated with a constant angular speed about an axis passing through its midpoint and perpendicular to its length. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the two ends of the rod is: Zero 1 2 B l 2 1 8 B l 2 B l 2 A metal ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. If the ring has a small cut (it is not a closed loop), the acceleration of the falling magnet is: Equal to g Less than g More than g Initially less than g and then more than g A circular coil of radius 0.1 m has 100 turns and carries a current of 5 A. It is placed in a uniform magnetic field of 0.5 T. If the coil is rotated through 180 from its position of stable equilibrium, the work done is: 1.57 J 3.14 J 0.785 J Zero The magnetic flux through a coil of resistance R changes by in time t . The total induced charge Q flowing through the coil depends on: and R only and t only , R and t R and t only The magnetic flux linked with a coil is and the total resistance of the circuit is R . The amount of charge that flows through the coil when the flux changes from 1 to 2 is: 2 - 1 R 2 - 1 Rt ( 2 - 1) R( 2 - 1) A circular disc of radius 0.2 m is placed in a uniform magnetic field of 1/ T in such a way that its axis makes an angle of 60 with B . The magnetic flux linked with the disc is: 0.02 Wb 0.04 Wb 0.01 Wb 0.08 Wb A magnet is dropped into a very long vertical copper tube. Ignoring air resistance, the magnet will: Eventually reach a constant terminal velocity Accelerate with acceleration g throughout Stop inside the tube Bounce back upwards A coil of area 100 cm 2 is kept at an angle of 30 with a magnetic field of 10 -1 T. The magnetic flux linked with the coil is: 5 10 -4 Wb 10 -3 Wb 8.66 10 -4 Wb 5 10 -3 Wb A bar magnet is dropped vertically through a horizontal copper ring. As the magnet enters the ring, the direction of the induced current (viewed from above) is: Anticlockwise Clockwise Zero First clockwise then anticlockwise An inductor L and a resistor R are connected to a DC source of emf E . The initial rate of increase of current ( dI/dt at t=0 ) is: E/L E/R E/ R 2 + L 2 Zero A DC motor has an armature resistance of 10 . When running at full speed on a 220 V supply, it draws 2 A. The back EMF produced is: 200 V 220 V 20 V 240 V A semi-circular conducting wire of radius R is rotated about its diameter with angular velocity in a uniform magnetic field B perpendicular to the diameter. The maximum induced EMF is: 1 2 B R 2 B R 2 1 4 B R 2 2 B R 2 The displacement current between the plates of a parallel plate capacitor of area A is I d . The rate of change of the electric field E between the plates is: I d / ( 0 A) I d 0 / A I d A / 0 0 A / I d A coil of N turns and area A is rotated with angular velocity in a uniform magnetic field B . The work done to rotate the coil from = 0 to = 90 (where is the angle between the normal to the coil and B ) is: NBA 2NBA Zero NBA/2 A circular loop of radius r is shrinking at a constant rate dr/dt = . A uniform magnetic field B exists perpendicular to the plane of the loop. The magnitude of the induced emf in the loop at any instant is: 2 r B r 2 B r B 2 B If the electric flux through a surface changes at a rate of 10 12 V m/s, the displacement current produced in the region (given 0 = 8.85 10 -12 F/m) is: 8.85 A 1.13 A 8.85 10 -24 A Zero A conductor of length l moves with a velocity v at an angle of 30 with the direction of a uniform magnetic field B . The induced emf across the ends of the conductor is: Blv/2 Blv 3 Blv/2 Zero A square conducting loop of side a and resistance R is placed in a magnetic field B = B 0 t perpendicular to its plane. The maximum current induced in the loop is: B 0 a 2 / R B 0 a 2 / R B 0 a / R B 0 a 2 R A metal rod of length l moves with velocity v in a magnetic field B . The velocity vector makes an angle with the magnetic field and the rod is perpendicular to the velocity. The motional emf induced is: B l v B l v B l v Zero The time constant of an LR circuit is 20 ms. The time taken for the current to grow to 1 - 1/e 2 (approximately 86.5 % ) of its maximum value is: 40 ms 20 ms 10 ms 60 ms The magnetic flux linked with a coil changes from 10 Wb to 2 Wb in 0.4 s. If the resistance of the coil is 4 , the amount of charge that flows through the coil is: 2 C 8 C 20 C 0.5 C The self-inductance of a coil is 5 mH. If the current in the coil changes from 1 A to 10 A in 10 -3 s, the induced emf is: 45 V 5 V 50 V 0.45 V A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic field B , constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is: Zero BLv/R clockwise BLv/R anti-clockwise 2BLv/R A coil is rotated in a uniform magnetic field. The induced emf is maximum when: The plane of the coil is parallel to the magnetic field The plane of the coil is perpendicular to the magnetic field The magnetic flux through the coil is maximum The angle between the field and the normal to the coil is 0 In an AC generator, a coil with N turns, all of area A and total resistance R , rotates with frequency f in a magnetic field B . The maximum value of current generated in the coil is: 2 f NBA / R NBA / R 2 f NBA f NBA / R A conducting rod of length L is rotating with constant angular velocity about an axis perpendicular to its length and passing through a point at distance L/4 from one of its ends. If a uniform magnetic field B exists parallel to the axis of rotation, the potential difference between the two ends of the rod is: 1 8 B L 2 1 2 B L 2 3 8 B L 2 Zero A square loop of side 10 cm is placed in a magnetic field which is increasing at a rate of 1.0 T/s. If the plane of the loop is inclined at 30 to the direction of the magnetic field, the induced emf in the loop is: 5.0 10 -3 V 1.0 10 -2 V 8.66 10 -3 V 2.5 10 -3 V An inductor of 5 mH has a current of 2 A flowing through it. If the current is reversed in 0.1 s, the average induced emf is: 0.2 V 0.1 V 0.4 V 0.05 V A circular loop of radius r is rotating about its diameter with angular frequency in a uniform magnetic field B perpendicular to the axis of rotation. The average power dissipated in the loop of resistance R over one cycle is: (B r 2 ) 2 2R (B r 2 ) 2 R B r 2 2R Zero The magnetic flux through a coil is given by = (t 3 - 4t 2 + 2t - 5) Wb. The time at which the induced emf is 6 V is: 2 s 1 s 3 s 0 s A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced: In sides AB and CD In sides AD and BC In all sides In no sides A horizontal straight wire of length L extending from East to West is falling freely with speed v . If the vertical component of Earth's magnetic field is B V and the horizontal component is B H , the emf induced in the wire is: B H L v B V L v B H 2 + B V 2 L v Zero In an AC generator, the phase difference between the magnetic flux linked with the coil and the induced emf is: /2 Zero /4 A metallic square loop of side a and resistance R moves with a uniform velocity v out of a region of uniform magnetic field B as shown. The force required to pull the loop at constant velocity is: B 2 a 2 v / R Bav / R B 2 a v / R 2 B a 2 v / R A square loop of side 10 cm and resistance 1 is moved with a velocity v in a uniform magnetic field of 0.1 T. If the induced current is 2 mA, the velocity v is: 0.2 m/s 0.02 m/s 2 m/s 20 m/s A rectangular, a square, a circular and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, V =v i . The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops, come out of the field region, will not remain constant for : any of the four loops The rectangular, circular and elliptical loops The circular and the elliptical loops Only the elliptical loop 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 :- Zero Bv r 2/2 and P is at higher potnetial rBv and R is at higher potential 2rBv and R is at higher potential A circular coil of radius 10 cm, 500 turns and resistance 2 is placed with its plane, perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180 in 0.25s. The induced e.m.f in the coil is (Take H E = 3.0 10 -5 T) : 6.6 10 -4 V 1.4 10 -2 V 2.6 10 -2 V 3.8 10 -3 V Electromagnetic induction is the phenomenon of production of induced emf in a coil when: Magnetic flux linked with the coil changes Current through the coil is constant The coil is placed in a static magnetic field The coil is placed in a static electric field A 800 turn coil of effective area 0.05 m 2 is kept perpendicular to a magnetic field 5 10 -5 T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be: 0.02 V 2 V 0.2 V 2 10 -3 , V 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 R 2 R 1 R 1 2 R 2 R 2 2 R 1 R 1 R 2 A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s -1 . If the vertical component of earth’s magnetic field at that place is 2 10 -5 T and electrical resistance of the coil is 12.56 , then the maximum induced current in the coil will be 1.5 A 1 A 2 A 0.25 A In the above diagram, 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: AB and DC BA and CD AB and CD BA and DC A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to: A. hold the sheet there if it is magnetic. B. hold the sheet there if it is non-magnetic. C. move the sheet away from the pole with uniform velocity if it is conducting. D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar. Choose the correct statement(s) from the options given below: B and D only A and C only A, C and D only C only A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is: Zero between the plates and non-zero outside Zero at all places Constant between the plates and zero outside the plates Non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates AB is a part of an electrical circuit (see figure). The potential difference “ V A - V B ”, at the instant when current i = 2 A and is increasing at a rate of 1 amp/second is: 10 volt 5 volt 6 volt 9 volt A thin semi-circular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B . The potential difference developed across the ring when its speed is v is: 2 r v B and P is at a higher potential than R 2 r v B and R is at a higher potential than P r v B and R is at a higher potential than P Zero The current in a self-inductance L = 2 mH is given by I = t 2 e -t . At what time is the induced emf zero? 2 s 1 s 4 s 3 s A square loop of side 10 cm and resistance 0.5 is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 0.70 s at a steady rate. The magnitude of induced current during this time interval is: 1 10 -3 A 2 10 -3 A 3 10 -3 A 4 10 -3 A