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**JEE Main Previous Year Papers Questions With Solutions Physics Electro Magnetic Induction**

**MuItipIe Choice with ONE correct answer**

**1.A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following [1985-2 marks]**

**a)The entire rod is at same electric potential.**

**b)There is an electric field in the rod**

**c)The electric potential is highest at the centre of the rod and increases towards its ends.**

**d)The electric potential is lowest at the centre of the rod and decreases towards its ends**

**Ans.**(b) Let the metal rod AB move parallel to x-axis. Let the uniform magnetic field point in positive z- direction. The free electrons of the metal rod will experience magnetic force towards B. So there will be excess of electrons on B- end and shortage of electrons on A-end. The end A becomes positively charged and the end B becomes negatively charged. An electric field is therefore setup in the metal rod. Option (b) is correct.

**2**.

**A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero ‘area, the charge flowing through the galvanometer is**

**[1995]**

**Ans.**

**3.A thin semicircular conducting ring of radius R is falling with its plane vertical in horizontal magnetic induction g , At the position MNQ the speed of the ring is v, and the potential difference developed across the ring is**

**Ans.**(d) At the position MNQ, the ring is at the point of moving out of the magnetic field. Its speed of fall is v. Due to fall, the flux associated with the ring changes. An emf is therefore induced in the ring.

**4.Two identical circular loops of metal wire are lyingon a table without touching each other, Loop-A carries a current which increases with time. In response, the loop-B. [JEE ’99 2 Marks]**

**a)remains stationary**

**b)is attracted by the loop-A**

**c)is repelled by the loop-A**

**d)rotates about its CM, with CM fixed**

**Ans.**(c)When the current in loop A increases, its magnetic field in the surrounding space increases. The flux linked with loop B therefore increases. An emf is induced in B. Under Lenz’s law, the current flows in B opposite to that in A. Due to opposite directions of currents in A and B, loop B is repelled by loop A.

**5.A coil of inductance 8.4 mil and resistance 6W is connected to a 12V battery. The current in the coil is 1.0 A at approximately the time [JEE’99-2 Marks]**

**a) 500 s**

**b) 25 s**

**c)35 ms**

**d)1 ms**

**Ans.**

**6.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 showm in the figure. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region. [2000-2 marks]**

**Ans.**

**7.**

**Ans.**

**8.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. [2001-2 marks]**

**Ans.**

**Ans.**(a)When current flows in one coil, the flux associated with the other coil depends upon its area receiving the flux. This is maximum in case (a) and so their mutual inductance will be maximum in situation (a).

**Ans.**(d)When switch S is closed a magentic field is set up in the space around P. The field lines threading Q increase in the direction from right to left and that field strength increases with time. According to Lenz’s law, I

_{Q1}should therefore flow in anticlockwise direction as seen by E. Reverse is the case when S is opened. I

_{Q2 }will be clockwise.

**11. 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 [JEE 2002(Scr), 2 Marks]**

**a) halved**

**b) the same**

**c) doubled**

**d) quadrupled**

**Ans.**(b)Current is induced in the short-circuited coil due to the imposed time-varying magentic field.

**Ans.**

**13. A small bar magnet is being slowly inserted with constant velocity inside a solenoid as shown in figure. Which graph best represents the relationship between emf induced with time? [2004- 2 M]**

**Ans.**(c) As the bar magnet is inserted inside a solenoid, flux associated with the solenoid increases. Induced emf is negative.

This emf increases as more length of the bar magnet is inserted in solenoid. Then emf starts decreasing. Polarity of emf will be opposite when the magnet enters and leaves the coil.

**14.A capacitor is charged using an external battery with a resistance x in series The dashed line shows the variation on In I with respect to time. If the resistance is changed to 2x, the new graph will be [2004 – 2 Marks]**

**Ans.**

**15**.

**A 4pF capacitor and a resistance of 5MQ are in series with 12V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given In (2) = 0.693]. [2005-2 marks]**

**Ans.**

**16.An infinitely long cylinder is kept parallel to auniform magnetic field g directed along positive z axis. The direction of induced current as seen from the z axis will be [2005 – 2 Marks ]**

**a).zero**

**b).anticlockwise of the +ve zaxis**

**c).clockwise of the + ve zaxis**

**d).along the magnetic field**

**Ans.**(a) The cylinder is not moving in stationary magnetic field. No emf is induced.The magentic filed applied to stationary cylinder is neither moving nor changing.No emf is induced in the cylinder.No current is induced in the cylinder.Induced current = zero.

**Ans.**

**18.An AC voltage source of variable angular frequency CO and fixed amplitude V**

_{0}is connected to series with a capacitance C and an electric bulb of resistance R (inductance zero). When CO is increased)**a) the bulb glows diammer**

**b) the bulb glows brighter**

**c) total bulb glows brighter**

**d) total impedance of the circuit increases**

**Ans.**

**19. The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. and I**

_{2}are the currents in the segments ab and cd. Then, [2009]**Ans**.(d)Since the field is increasing, the flux region is increasing; the induced current (by Lenz law) should flow in an anticlockwise sense around the boundary of the shaded region.

**Multiple Choice with ONE or MORE THAN ONE correct answers**

**20.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 induction ~g, constant in time and space, pointing perpendicular and into the plane of the loop exists every where. The current induced in the loop is [1989-2 marks]**

**Ans.**The square loop moves in its plane.A uniform magnetic induction exists in the plane of the loop. Hence change in magnetic flux is zero. Induced current in the loop = zero.

**21. Two different coils have self inductances Lj = 8mH and 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 constant 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 ip Vj and W_{(}respectively. Corresponding values for the second coil at the same instant are i_{2}, v_{2}and W_{2}respectively. Then:**Ans.**

**22. A small square loop of wire of side l is placed inside a large square loop of wire of side L(L»Z). The loops are co-planar & their centres coincide. The mutual inductance of the system is proportional to**

**[1998- 2 Marks]**

**Ans.**

**23.A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following**

**a)the entire rod is at the same electric potential**

**b)There is an electric field in the rod**

**c)The electric potential is highest at the centre of the rod & decreases towards its ends**

**d)The electric potential is lowest at the centre of the rod & increases towards its ends**

**Ans.**

**24. A field line is shown in the figure. This field cannot represent**

**a)magnetostatic field**

**b)electrostatic field**

**c)induced electric field**

**d)gravitational field**

**Ans.**

**25.Two metallic rings A and B, identical in shape and size but having different resistivities p**

_{A}and p_{B}, are kept on top of two identical solenoids as shown in the figure. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights h_{A}and h_{B}, respectively, with h_{A}> h_{B}. The possible relation(s) between their resistivities and their masses m_{A}and m_{B}is (are) [2009]**Ans.**

**26.A series R-C circuit is connected to AC voltage source. Consider two cases ; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current I**

_{R}through the resistor and voltage V_{c}across the capacitor are compared in the two cases. Which of the following is / are true ?**Ans.**

**Assertion – Reasoning type**

**Instructions :**The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if

a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1

b)Statement-l and2 are true and statement-2 is not a correct explanation for statement-1

c)Statement-1 is true, statement-2 is Base

d)Statement-1 is false, statement-2 is true.

**27.Statement – 1 : A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure.The ring can float at a certain height above the coil. [2007]**

**Because Statement – 2 : In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.**

**a)Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explantation for Statement- 1.**

**b)Statement – 1 is True, Statement – 2 is True; Statement -2 is NOT a correct explanation for Statement-1.**

**c)Statement – 1 is True, Statement – 2 is False.**

**d)Statement – 1 is False, Statement -2 is True.**

**Ans.**(a) The induced current in the ring will interact with horizontal component of magnetic field and both will repel each other. This repulsion will balance the weight of the ring.

**Comprehension based question**

**Read the passage given below and answer the questions that follow :**

In the given circuit the capacitor (C) may be charged through resistance R by battery V by closing switch S1. Also when S1 is opened and S

_{2}is closed the capacitor is connected in series with inductor (L).

**Ans.**

**Ans.**(d) When the capacitor gets fully charged S is opened and S

_{2}is closed. Capacitor gets discharged.

**Ans.**

**Matching type**

**31.You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the furs two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current I (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage and V**

_{2}. (indicated in circuits) are related as shown in Column I. Match the two**Ans.**

**32.Column I gives certain situations in whcih a straight metallic wire of resistance R is used and column II gives some resulting effects. Match the statements in column I with the statements in column II. [2007-6 marks]**

**Ans.**

**Subjective / Numerical integer type**

**33.A current from A to B is increasing in magnitude. What is the direction of induced current, in the loop as shown in the figure? [1979]**

**Ans.**The direction of the induced current is as shown in the figure, according to Lenz’s law which states that the indeed current flows always in such a direction as to oppose the change which is giving rise to it.

**34.The two rails of a railway track, insulated from each other and the ground, are connected to a millivolt meter. What is the reading of the milli voltmeter when a train travels at a speed of 180 km/hour along the track, given that the horizontal components of earth’s magnetic field is 0.2 x 10-**

^{4}weber / m^{2}and the rails are separated by 1 metre? [1981 – 4 Marks]**Ans.**

**35.Three ideitical closed coils A, B and C are placed and C cairy equal currents as shown in fig. Coils B and C are fixed in position and coil A is moved direction of the induced current in the diagram.[1982 – 2 Marks]**

**Ans.**Coils B and C are fixed. When the coil A is moved towards the parallel coil B, at uniform speed, the magnetic flulx linked with B changes. An induced e.m.f. is setup in B and an induced current flows in B.

Under the phenomenon of induction, the induced current in 5 will flow so as to oppose the cause which produces it.Hence current in 5 will be in a direction opposite to that of . The direction of induced current is marked in the figure.

**36.A sqiare metal wire loop of side 10 cm and resistaice 1 ohm is moved with a constant velocity v**

_{0}in a uniform magnetic field of induction B = 2 weber / m^{2}as shown in the figure. The magnetic field lines are perpendicular to the plane of the loop (directed into the paper). The’ loop is connected to a network of resistors each of value 3 ohm. The resistances of the lead wires OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 milli ampere in the loop? Give the direction of current in the loop. [1983-6 marks]**Ans.**

**37.Space is divided by the line AD into two regions. Region I is field free and the Region II has a uniform magnetic field B directed into the plane of the paper. ACD is a semicircular conducting loop of radius r with centre at O, the plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity u about an axis passing through O and the perpendicular to the plane of the paper. The effective resistance of the loop is R. [1985-6 marks]**

**i)Obtain an expression for the magnitude of the induced current in the loop.**

**ii)Show the direction of the current when the loop is entering into the Region II.**

**iii)Plot a graph between the induced emf and the time of rotation for two periods of rotation.**

**Ans.**

**Ans.**

**Ans.**

**Ans.**

**41.Two parallel vertical metallic rails AB & CD are separated by 1 m. They are connected at two ends by resistance R**

_{1}& R_{2}as shown in the figure. A horizontal metallic bar L of mass 0.2 kg slides without friction, vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of 0.6T perpendicular to the plane of the rails. It is observed that when the terminal velocity is attained, the powers dissipated in R_{1}& R_{2}are 0.76 W & 1.2 W respectively. Find the terminal velocity of bar L & the values of R1 & R_{2}.[1994, 6 Marks]**Ans.**

**42.A metal rod OA of mass m & length r is kept rotating with a constant angular speed v in a vertical plane about a horizontal axis at the end O. The free end A is arranged to slide without friction along a fixed conducting circular ring in the same plane as that of rotation. A uniform & constait magnetic induction B is applied perpendicular & into the plane of rotation as shown in figure. An inductor L and an external resistance R are connected through a switch S between the point O & a point C on the ring to form an electrical circuit. Neglect the resistance of the ring and the rod. Initially, the switch is open. [1995-10 Marks]**

**Ans.**OA is metal rod which rotates with a constant angular speed cc . The free end A of rod OA slides along a fixed conducting circular ring, g is the uniform and constant magnetic induction applied perpendicular and into the plane of rotation of the rod.(a) Induced emf across switch S :

**43.A solenod has an inductance of 10 Henry & a resistance of 2 W. It is connected to a 10 volt battery. Sow long will it take for the magnetic energy to reach 1/4 of its maximum value ?[1996-3 Marks]**

**Ans.**

**44.An infiritesimally small bar magnet of dipole moment M is pointing and moving with the speed v in the x-direction. A small closed circular conducing loop of radius a and negligible self- inductance lies in the y-z plane with its centre at x = 0, aid its axis coinciding with the x-axis. Find the force opposing the motion of the magnet, if the resistance of the loop is R. Assume that the distant of x of the magnet from the centre of the loop s much greater than a. [1997- 5 Marks]**

**Ans.**A closed circular conducting loop lies in the y — z plane with its centre at x = 0 . A small bar magnet moves with the speed v in the x— direction.Magnetic lines of the moving bar magnet thread the loop. An induced emf is therefore developed in the loop and an induced current flows in the closed loop.

Positive sign of force denotes repulsion between the magnet and the coil.

**45.A par of parallel horizontal conducting rails of neglgible resistance, shorted at one end is fixed on a table. The distance between the rails is L. A concucting massless rod of resistance R can slide on he rails frictionlessly. The rod is tied to a masless string which passes over a pulley fixed to he edge of the table. A mass m, tied to the otler end of the string, hangs vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate:**

**i)the terminal velocity achieved by the rod.**

**ii)the acceleration of the mass at the instant when the velocity of the rod, is half the terminal velocity.[1997 – 5 Marks]**

**Ans.**

**Ans.**

**Ans.**

**48.A thermocole vessel contains 0.5 kg of distilled water at 30° C • A metal coil of area 5 x 10**

^{3}m^{2}number of turns 100, mass 0.06 kg and resistance 1.6 ohms is lying horizontally at the bottom of the vessel. A uniform time varying magnetic field is setup to pass vertically through the coil at time t=0. The field is first increased from zero to 0.8T at a constant rate between 0 and 0.2s and then decreased to 0 and the same rate between 0.2 and 0.4s. This cycle is repeated 12000 times. Make sketches of the current through the coil and the power dissipated in the coil as function of time for the first two cycles. Clearly indicate the magnitudes of the quantities on the axes. Assume that no heat is lost to the vessel or the surroundings. Determine the final temperature of the water under thermal equilibrium. Specific heat of metal = 500 J kg^{-1}K^{-1}and the specific heat of water =4200 J kg^{-1}K^{-1}. Neglect the inductance of the coil. [2000-10 marks]**Ans.**

**49.An inductor of inductance L = 400 mH and resistors of resistance R1 = 2W and R**

_{2}= 2W are connected to a battery of e.m.f. E = 12V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at time t = 0. What is the potential drop across L as a function of time? After the steady state is reached, the switch is opened. What is the direction and the magnitude of current through R_{1}as a function of time?[2001-5 Marks]**Ans.**

**50.A rectangular loop PQRS, made from a uniform wire, has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y — axis (see figure).**

**Ans.**A loop PQRS is held in the x— y plane. It is free to rotate about arm PQ which remains hinged along y — axis. A current / is passed through it. When the loop is released, it stays in horizontal position in equilibrium.(a) Direction of current I in PQ .Let the direction of current I in PQ be from P to Q in the wire PQ. The loop develops a mag¬netic moment = M

**51.A metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straigit wire carrying a constant current I**

_{0}is placed in tie plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x_{1}from the long wire. At t=0, it is made to slide 01 the rails away from the wire. [1002- 5 Marks]**Ans.**

**52.**

**Ans.**

**53.In the figure both cells A and B are of equal emf E. Find R for which potential difference across battery A will be zero, long time after the switch S is closed. Internal resistance of batteries A and B are r**

_{1}and r_{2}respectively, ( r_{1}> r_{2}).[2004 – 4 Marks]**Ans.**The circuit contains resistances, inductance and capacitance as shown in the figure.

When current flows for a long time the capacitor will be fully charged. Resistance across capacitor becomes infinite and no current passes through it. Resistance across inductor is zero for D.C. and the whole current passes through it.

**Ans.**

**Ans.**

**True/ False type**

**56.An e.m.f. can be induced between the two ends of a straight copper wire when it is moved through a uniform magnetic field. [1980]**

**Ans.**True : It the conductor cuts the lines of force.

**57.A coil of metal wire is kept stationary in a non uniform magnetic field. An emf is induced in the coil. [1986-3 marks]**

**Ans.**false :The coil of metal wire is stationary in a non-uniform magnetic field. The magnetic flux linked with the coil does not change.An emf is therefore not induced in the coil.The statement is false.

**58.A conducting rod AB moves parallel to the x-axis (see figure) in a uniform magnetic field pointing in the positive z-direction. The end A of the rod gets positively charged. [1987-2 Marks]**

**Ans.**false :The coil of metal wire is stationary in a non-uniform magnetic field. The magnetic flux linked with the coil does not change. An emf is therefore not induced in the coil. The statement is false.

Therefore at g, there will be an excess of elections and at 4 there will be a deficiency of electrons. The end A of the rod gets positively charged because deficiency of electrons means a positive charge. The statement is true.

**Fill in blanks**

**59.A uniformly wound solenoidal coil of self inductance 1,8 xl0-**

^{4}henry and resistance 6 ohm is broken up into two identical coils. These identical coils are then connected in parallel a cross a 15 volt battery of negligible resistance. The time constant for the current in the circuit is second and the steady state current through the battery is……………..ampere. [1989-2 marks]**Ans.**

**60.In a straight conducting wire, a constant current is flowing from left to right due to a source of emf. When the source is switched off, the direction of the induced current in the wire will be………………………………….[1993-1 mark]**

**Ans.**When the source is switched off, current flowing from left to right in the conducting wire decreases to zero. According to Lenz’s law’, induced currrent will oppose the cause. Consequently the direction of induced current in the wire will be from left to right.

**Ans.**

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