JEE Main & Advanced Physics Electro Magnetic Induction Question Bank

done Critical Thinking Total Questions - 48

• question_answer1)
  An electron moves along the line AB, which lies in the same plane as a circular loop of conducting wires as shown in the diagram. What will be the direction of current induced if any, in the loop         [MP PET 1989; AIIMS 1982, 2001; KCET 2003;  UPSEAT 2005]
  A)
             No current will be induced done clear
  B)
             The current will be clockwise done clear
  C)
             The current will be anticlockwise done clear
  D)
             The current will change direction as the electron passes by done clear
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• question_answer2)
  A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity \[\omega \]. The induced e.m.f. between the two ends is [MP PMT 1992; Orissa JEE 2003]
  A)
             \[\frac{1}{2}B\omega {{l}^{2}}\]                                       done clear
  B)
             \[\frac{3}{4}B\omega {{l}^{2}}\] done clear
  C)
             \[B\omega {{l}^{2}}\]        done clear
  D)
             \[2B\omega {{l}^{2}}\] done clear
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• question_answer3)
  Two different coils have self-inductance \[{{L}_{1}}=8\]mH, \[{{L}_{2}}=2mH\]. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage and the energy stored in the first coil are \[{{i}_{1}},\ {{V}_{1}}\]and \[{{W}_{1}}\]respectively. Corresponding values for the second coil at the same instant are \[{{i}_{2}},\ {{V}_{2}}\] and \[{{W}_{2}}\] respectively. Then                                                [IIT JEE 1994]
  A)
             \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{1}{4}\]                       done clear
  B)
             \[\frac{{{i}_{1}}}{{{i}_{2}}}=4\]8 done clear
  C)
             \[\frac{{{W}_{2}}}{{{W}_{1}}}=4\]                                   done clear
  D)
             \[\frac{{{V}_{2}}}{{{V}_{1}}}=\frac{1}{4}\] done clear
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• question_answer4)
  An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time \[t=\infty \] and at t = 1 second is       [MP PMT 1994]
  A)
             \[\frac{{{e}^{1/2}}}{{{e}^{1/2}}-1}\]                               done clear
  B)
             \[\frac{{{e}^{2}}}{{{e}^{2}}-1}\] done clear
  C)
             \[1-{{e}^{-1}}\]                    done clear
  D)
             \[{{e}^{-1}}\] done clear
  View Solution play_arrow

• question_answer5)
  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   [MP PMT 1994; MP PET 2001]
  A)
             \[{{R}_{1}}/{{R}_{2}}\]      done clear
  B)
             \[{{R}_{2}}/{{R}_{1}}\] done clear
  C)
             \[R_{1}^{2}/{{R}_{2}}\]     done clear
  D)
             \[R_{2}^{2}/{{R}_{1}}\] done clear
  View Solution play_arrow

• question_answer6)
  A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position MNQ, the speed of the ring is V and the potential difference developed across the ring is [IIT JEE 1996]
  A)
             Zero done clear
  B)
             \[B\nu \pi {{R}^{2}}/2\] and M is at higher potential done clear
  C)
             \[\pi RBV\]and Q is at higher potential done clear
  D)
             2RBV and Q is at higher potential done clear
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• question_answer7)
  At a place the value of horizontal component of the earth's magnetic field H is \[3\times {{10}^{-5}}\,Weber/{{m}^{2}}\]. A metallic rod AB of length 2 m placed in east-west direction, having the end A towards east, falls vertically downward with a constant velocity of 50 m/s. Which end of the rod becomes positively charged and what is the value of induced potential difference between the two ends                              [MP PET 1996]
  A)
             End A, \[3\times {{10}^{-3}}\,mV\]                                 done clear
  B)
             End A, 3 mV done clear
  C)
             End B, \[3\times {{10}^{-3}}\,mV\]                                 done clear
  D)
             End B, 3 mV done clear
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• question_answer8)
  Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will                                    [MP PMT 1999]
  A)
             Increase done clear
  B)
             Remain the same done clear
  C)
             Decrease done clear
  D)
             Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it done clear
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• question_answer9)
  A circular loop of radius R carrying current I lies in x-y plane with its centre at origin. The total magnetic flux through x-y plane is                                                   [IIT-JEE 1999]
  A)
             Directly proportional to I done clear
  B)
             Directly proportional to R done clear
  C)
             Directly proportional to \[{{R}^{2}}\] done clear
  D)
             Zero done clear
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• question_answer10)
  Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A carries a current which increases with time. In response, the loop-B [IIT JEE 1999; UPSEAT 2003]
  A)
             Remains stationary done clear
  B)
             Is attracted by the loop-A done clear
  C)
             Is repelled by the loop-A done clear
  D)
             Rotates about its CM, with CM fixed (CM is the centre of mass) done clear
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• question_answer11)
  Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation \[I={{I}_{0}}\sin \omega \,t\], where \[{{I}_{0}}=10A\] and w = 100 p radian/sec. The maximum value of e.m.f. in the second coil is [CBSE PMT 1998; Pb. PMT 2000]
  A)
             2p   done clear
  B)
             5p done clear
  C)
             p     done clear
  D)
             4p done clear
  View Solution play_arrow

• question_answer12)
  A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to                            [IIT JEE 1998]
  A)
             l / L                                            done clear
  B)
             \[{{l}^{2}}/L\] done clear
  C)
             \[L/l\]                                       done clear
  D)
             \[{{L}^{2}}/l\] done clear
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• question_answer13)
  A wire of length 1 m is moving at a speed of 2ms?1 perpendicular to its length and a homogeneous magnetic field of 0.5 T. The ends of the wire are joined to a circuit of resistance 6 W. The rate at which work is being done to keep the wire moving at constant speed is    [Roorkee 1999]
  A)
             \[\frac{1}{12}W\]                done clear
  B)
             \[\frac{1}{6}W\] done clear
  C)
             \[\frac{1}{3}W\]                  done clear
  D)
             1W done clear
  View Solution play_arrow

• question_answer14)
  A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region                                              [IIT-JEE (Screening) 2000]
  A)
             Is zero done clear
  B)
             Decreases as \[\frac{1}{r}\] done clear
  C)
             Increases as r done clear
  D)
             Decreases as \[\frac{1}{{{r}^{2}}}\] done clear
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• question_answer15)
  A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current \[{{I}_{1}}(t)\] starts flowing through the coil. If \[{{I}_{2}}(t)\] is the current induced in the ring. and \[B(t)\] is the magnetic field at the axis of the coil due to \[{{I}_{1}}(t),\] then as a function of time (t > 0), the product I2 (t) B(t) [IIT-JEE (Screening) 2000]
  A)
             Increases with time           done clear
  B)
             Decreases with time done clear
  C)
             Does not vary with time   done clear
  D)
             Passes through a maximum done clear
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• question_answer16)
  Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be [IIT JEE (Screening) 2001]
  A)
             Maximum in situation       done clear
  B)
             Maximum in situation done clear
  C)
             Maximum in situation       done clear
  D)
             The same in all situations done clear
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• question_answer17)
  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                [IIT JEE (Screening) 2001]
  A)
             In AD, but not in BC done clear
  B)
             In BC, but not in AD done clear
  C)
             Neither in AD nor in BC done clear
  D)
             In both AD and BC done clear
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• question_answer18)
  A conducting rod of length 2l is rotating with constant angular speed w about its perpendicular bisector. A uniform magnetic field \[\overrightarrow{B}\] exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is [MP PET 2001]
  A)
             Bwl2                                          done clear
  B)
             \[\frac{1}{2}B\omega {{l}^{2}}\] done clear
  C)
             \[\frac{1}{8}B\omega {{l}^{2}}\]                                       done clear
  D)
             Zero done clear
  View Solution play_arrow

• question_answer19)
  An inductor of 2 henry and a resistance of 10 ohms are connected in series with a battery of 5 volts. The initial rate of change of current is                                                 [MP PMT 2001]
  A)
             0.5 amp/sec                          done clear
  B)
             2.0 amp/sec done clear
  C)
             2.5 amp/sec                          done clear
  D)
             0.25 amp/sec done clear
  View Solution play_arrow

• question_answer20)
  As shown in the figure, P and Q are two coaxial conducting loops separated by some distance. When the switch S is closed, a clockwise current \[{{I}_{P}}\] flows in P (as seen by E) and an induced current \[{{I}_{{{Q}_{1}}}}\] flows in Q. The switch remains closed for a long time. When S is opened, a current \[{{I}_{{{Q}_{2}}}}\] flows in Q. Then the directions of \[{{I}_{{{Q}_{1}}}}\] and \[{{I}_{{{Q}_{2}}}}\] (as seen by E) are                     [IIT JEE (Screening) 2002]
  A)
             Respectively clockwise and anticlockwise done clear
  B)
             Both clockwise done clear
  C)
             Both anticlockwise done clear
  D)
             Respectively anticlockwise and clockwise done clear
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• question_answer21)
  A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be                                                        [IIT-JEE (Screening) 2002]
  A)
             Halved                                     done clear
  B)
             The same done clear
  C)
             Doubled                                  done clear
  D)
             Quadrupled done clear
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• question_answer22)
  A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing area 0.01 m2 in such a way that the plane of the necklace is normal to the field and is having a resistance R = 0.01 W. Because of power failure, the field decays to 1 T in time 10?3 seconds. Then what is the total heat produced in her necklace ? (T = Tesla) [Orissa JEE 2002]
  A)
             10 J                                            done clear
  B)
             20 J done clear
  C)
             30 J                                            done clear
  D)
             40 J done clear
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• question_answer23)
  A coil of inductance 8.4 mH and resistance 6 W is connected to a 12 V battery. The current in the coil is 1.0 A at approximately the time  [IIT-JEE (Screening) 1999; UPSEAT 2003]
  A)
             500 sec                                     done clear
  B)
             20 sec done clear
  C)
             35 milli sec                              done clear
  D)
             1 milli sec done clear
  View Solution play_arrow

• question_answer24)
  As shown in the figure a metal rod makes contact and complete the circuit. The circuit is perpendicular to the magnetic field with \[B=0.15\,tesla.\] If the resistance is \[3\,\Omega \], force needed to move the rod as indicated with a constant speed of \[2m/sec\] is                                                               [MP PET 1994]
  A)
             \[3.75\times {{10}^{-3}}\]N    done clear
  B)
             \[3.75\times {{10}^{-2}}\,N\] done clear
  C)
             \[3.75\times {{10}^{2}}\,N\]  done clear
  D)
             \[3.75\times {{10}^{-4}}N\] done clear
  View Solution play_arrow

• question_answer25)
  Two identical coaxial circular loops carry current i each circulating in the clockwise direction. If the loops are approaching each other, then                                                [MP PMT 1995, 96]
  A)
             Current in each loop increases done clear
  B)
             Current in each loop remains the same done clear
  C)
             Current in each loop decreases done clear
  D)
             Current in one-loop increases and in the other it decreases done clear
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• question_answer26)
  In the following figure, the magnet is moved towards the coil with a speed v and induced emf is e. If magnet and coil recede away from one another each moving with speed v, the induced emf in the coil will be
  A)
             e done clear
  B)
             2e done clear
  C)
             e/2 done clear
  D)
             4e done clear
  View Solution play_arrow

• question_answer27)
  A current carrying solenoid is approaching a conducting loop as shown in the figure. The direction of induced current as observed by an observer on the other side of the loop will be
  A)
              Anticlockwise                    done clear
  B)
              Clockwise done clear
  C)
              East                                        done clear
  D)
              West done clear
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• question_answer28)
  A conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are
  A)
             B to A and D to C               done clear
  B)
             A to B and C to D               done clear
  C)
             A to B and D to C               done clear
  D)
             B to A and C to D done clear
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• question_answer29)
  A square metallic wire loop of side 0.1 m and resistance of 1W is moved with a constant velocity in a magnetic field of 2 wb/m2 as shown in figure. The magnetic field is perpendicular to the plane of the loop, loop is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of 1mA in loop
  A)
             1 cm/sec                               done clear
  B)
             2 cm/sec done clear
  C)
             3 cm/sec                               done clear
  D)
             4 cm/sec done clear
  View Solution play_arrow

• question_answer30)
  A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of 1 wb/m2, as shown in fig. If all the four sides are of 1m length each, then the induced emf between points A and D is
  A)
            0       done clear
  B)
            1.41 volt done clear
  C)
            0.71 volt                                 done clear
  D)
            None of the above done clear
  View Solution play_arrow

• question_answer31)
  A conducting rod PQ of length L = 1.0 m is moving with a uniform speed v = 2 m/s in a uniform magnetic field \[B=4.0\,T\] directed into the paper. A capacitor of capacity C = 10 mF is connected as shown in figure. Then
  A)
            qA = + 80 mC and qB = ? 80 mC done clear
  B)
            qA = ? 80 mC and qB = + 80 mC done clear
  C)
            qA = 0 = qB done clear
  D)
            Charge stored in the capacitor increases exponentially with time done clear
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• question_answer32)
  The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is 10W. The current in the circuit will be now
  A)
              i = 0.5 A                                done clear
  B)
              i > 0.5 A done clear
  C)
              i < 0.5 A                                done clear
  D)
              i = 0 done clear
  View Solution play_arrow

• question_answer33)
  Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction \[B={{B}_{0}}{{e}^{-t}}\] is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to
  A)
              \[\frac{B_{0}^{2}\pi {{r}^{2}}}{R}\]                                               done clear
  B)
              \[\frac{{{B}_{0}}10{{r}^{3}}}{R}\] done clear
  C)
              \[\frac{B_{0}^{2}{{\pi }^{2}}{{r}^{4}}R}{5}\]                              done clear
  D)
              \[\frac{B_{0}^{2}{{\pi }^{2}}{{r}^{4}}}{R}\] done clear
  View Solution play_arrow

• question_answer34)
  A conducting ring is placed around the core of an electromagnet as shown in fig. When key K is pressed, the ring
  A)
              Remain stationary done clear
  B)
              Is attracted towards the electromagnet done clear
  C)
              Jumps out of the core done clear
  D)
              None of the above done clear
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• question_answer35)
  The north and south poles of two identical magnets approach a coil, containing a condenser, with equal speeds from opposite sides. Then
  A)
              Plate 1 will be negative and plate 2 positive done clear
  B)
              Plate 1 will be positive and plate 2 negative done clear
  C)
              Both the plates will be positive done clear
  D)
              Both the plates will be negative done clear
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• question_answer36)
  A highly conducting ring of radius R is perpendicular to and concentric with the axis of a long solenoid as shown in fig. The ring has a narrow gap of width d in its circumference. The solenoid has cross sectional area A and a uniform internal field of magnitude B0. Now beginning at t = 0, the solenoid current is steadily increased to so that the field magnitude at any time t is given by B(t) = B0 + at where \[\alpha >0\]. Assuming that no charge can flow across the gap, the end of ring which has excess of positive charge and the magnitude of induced e.m.f. in the ring are respectively
  A)
              X, Aa done clear
  B)
              X pR2a done clear
  C)
              Y, pA2a done clear
  D)
              Y, pR2a done clear
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• question_answer37)
  Plane figures made of thin wires of resistance R = 50 milli ohm/metre are located in a uniform magnetic field perpendicular into the plane of the figures and which decrease at the rate dB/dt = 0.1 m T/s. Then currents in the inner and outer boundary are. (The inner radius a = 10 cm and outer radius b = 20 cm) 
  A)
              10? 4 A (Clockwise), 2 ´ 10? 4 A (Clockwise) done clear
  B)
              10? 4 A (Anticlockwise), 2 ´ 10? 4 A (Clockwise) done clear
  C)
              2 ´ 10? 4 A (clockwise), 10? 4 A (Anticlockwise) done clear
  D)
              2 ´ 10? 4 A (Anticlockwise), 10? 4 A (Anticlockwise) done clear
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• question_answer38)
  A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2T perpendicular to the plane of loop. Resistance of connector is r = 2W. Two resistance of 6W and 3W are connected as shown in figure. The external force required to keep the connector moving with a constant velocity v = 2m/s is
  A)
              6 N done clear
  B)
              4 N done clear
  C)
              2 N done clear
  D)
              1 N done clear
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• question_answer39)
  A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of
  A)
              \[\frac{mgR}{Bl}\] done clear
  B)
              \[\frac{mgR}{{{B}^{2}}{{l}^{2}}}\] done clear
  C)
              \[\frac{mgR}{{{B}^{3}}{{l}^{3}}}\] done clear
  D)
              \[\frac{mgR}{{{B}^{2}}l}\] done clear
  View Solution play_arrow

• question_answer40)
  A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field \[\vec{B}\] directed into the paper. AO = l and OC = 3l. Then
  A)
             \[{{V}_{A}}-{{V}_{O}}=\frac{B\omega {{l}^{2}}}{2}\] done clear
  B)
             \[{{V}_{O}}-{{V}_{C}}=\frac{7}{2}B\omega {{l}^{2}}\] done clear
  C)
             \[{{V}_{A}}-{{V}_{C}}=4B\omega {{l}^{2}}\] done clear
  D)
             \[{{V}_{C}}-{{V}_{O}}=\frac{9}{2}B\omega {{l}^{2}}\] done clear
  View Solution play_arrow

• question_answer41)
  How much length of a very thin wire is required to obtain a solenoid of length \[{{l}_{0}}\] and inductance L
  A)
             \[\sqrt{\frac{2\pi L{{l}_{0}}}{{{\mu }_{0}}}}\]              done clear
  B)
             \[\sqrt{\frac{4\pi L{{l}_{0}}}{\mu _{0}^{2}}}\] done clear
  C)
             \[\sqrt{\frac{4\pi L{{l}_{0}}}{{{\mu }_{0}}}}\]              done clear
  D)
             \[\sqrt{\frac{8\pi L{{l}_{0}}}{{{\mu }_{0}}}}\] done clear
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• question_answer42)
  What is the mutual inductance of a two-loop system as shown with centre separation l
  A)
              \[\frac{{{\mu }_{0}}\pi {{a}^{4}}}{8{{l}^{3}}}\] done clear
  B)
              \[\frac{{{\mu }_{0}}\pi {{a}^{4}}}{4{{l}^{3}}}\] done clear
  C)
              \[\frac{{{\mu }_{0}}\pi {{a}^{4}}}{6{{l}^{3}}}\] done clear
  D)
              \[\frac{{{\mu }_{0}}\pi {{a}^{4}}}{2{{l}^{3}}}\] done clear
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• question_answer43)
  The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first
  A)
              (i) \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\,\,({{i}_{1}}=0)\] (ii) \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\] done clear
  B)
              (i) \[{{i}_{2}}<{{i}_{3}}<{{i}_{1}}\,\,({{i}_{1}}\ne 0)\] (ii) \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\] done clear
  C)
              (i) \[{{i}_{2}}={{i}_{3}}={{i}_{1}}\,\,({{i}_{1}}=0)\] (ii) \[{{i}_{2}}<{{i}_{3}}<{{i}_{1}}\] done clear
  D)
              (i) \[{{i}_{2}}={{i}_{3}}>{{i}_{1}}\,\,({{i}_{1}}\ne 0)\] (ii) \[{{i}_{2}}>{{i}_{3}}>{{i}_{1}}\] done clear
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• question_answer44)
  The network shown in the figure is a part of a complete circuit. If at a certain instant the current i is 5 A and is decreasing at the rate of \[{{10}^{3}}A/s\] then \[{{V}_{A}}-{{V}_{B}}\] is
  A)
              5 V done clear
  B)
              10 V done clear
  C)
              15 V done clear
  D)
              20 V done clear
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• question_answer45)
  A 50 volt potential difference is suddenly applied to a coil with \[L=5\times {{10}^{-3}}\] henry and \[R=180\,ohm\]. The rate of increase of current after 0.001 second is [MP PET 1994]
  A)
             27.3 amp/sec                        done clear
  B)
             27.8 amp/sec done clear
  C)
             2.73 amp/sec                        done clear
  D)
             None of the above done clear
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• question_answer46)
  The current in a LR circuit builds up to \[\frac{3}{4}\]th of its steady state value in \[4s\]. The time constant of this circuit is [Roorkee 2000]
  A)
             \[\frac{1}{\ln 2}s\]              done clear
  B)
             \[\frac{2}{\ln 2}s\] done clear
  C)
             \[\frac{3}{\ln 2}s\]              done clear
  D)
             \[\frac{4}{\ln 2}s\] done clear
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• question_answer47)
  A conducting ring of radius 1 meter is placed in an uniform magnetic field B of 0.01Telsa oscillating with frequency 100Hz with its plane at right angles to B. What will be the induced electric field                                [AIIMS 2005]
  A)
             \[\pi \,volt/m\]                    done clear
  B)
             \[2\,volt/m\] done clear
  C)
             \[10\,volt/m\]                      done clear
  D)
             \[62\,volt/m\] done clear
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• question_answer48)
  A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle \[2\theta \]. The earth?s magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is                           [MP PET 2005]
  A)
             \[2BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{1/2}}\]        done clear
  B)
             \[BL\sin \left( \frac{\theta }{2} \right)(gL)\] done clear
  C)
             \[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{3/2}}\]           done clear
  D)
             \[BL\sin \left( \frac{\theta }{2} \right){{(gL)}^{2}}\] done clear
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