## JEE Main Previous Year Papers Questions With Solutions Physics Electromagnetism

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Ans.(d) A current I1, flows in anticlockwise direction while I2 flows in clockwise direction through the two portions of the ring. The fields due to I1 and will be in opposite directions at O.

Ans.(a) The magnetic force on the charged particles provides necessary centripetal force for circular motion of the particles.
4.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 [1999-2 marks]
a)directly proportional to I
b)directly proportional to R
c)inversely proportional to R
d) zero
Ans.(d) Total magnetic flux passing through whole of the x — y plane will be zero.The magnetic lines form a closed loop. The number of lines moving downwards in x — y plane will be same in number to that coming upwards from the x-y plane. Net flux will therefore be zero.
5.A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a   [JEE’99, 2]
a) straight line b) circle c) helix d) cycloid
Ans.(a) Uniform electric and magnetic fields are parallel to each other.The electric field will accelerate or decelerate the charged particle parallel to itself. The charged particle will move parallel to electric field and so parallel to magnetic field. The magnetic force on such charged particle will be zero. Path of particle will be a straight line.
6.A particle of charge q and mass m moves in a circular orbit of radius r with angular speed uj . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on[2000-2 marks]
a) w and q      b) w, q and m
c) q and m     d) w and m
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7.Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper, as shown. The variation of the magnetic field B along the line XX ’ given by          [2000-2 marks]

Ans.(b) The steady currents in the two parallel wires flow out of paper. 0 is a point in the centre between two wires. The wires are at P and Q. Since the current flows out of paper, the magnetic field at points to the right of given wire will be upwards and to the left will be downwards.
8.An infinitely long conductor PQR is bent to form a right angle as shown in figure. A current I flows through PQR. The magnetic field due to this current at the point M is H,. Now, another infinitely long straight conductor QS is connected at Q so that the current is I/2 m QR as well as in QS, the current in PQ remaining unchanged. The magnetic field at M is now H2 The ratio H1/H2] is

Ans.(c) Initially currents in PQ and QR set up magnetic fields at M
9.An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the +z direction, then   [2000-2 marks]
a)positive ions deflect towards +y direction and negative ions towards -y direction
b)all ions deflect towards -y direction.
c)all ions deflect towards -y direction
d)positive ions deflect towards -y direction and negative ions towards +y direction.
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10.A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point (a, 0, a) points in the direction [2001-2 marks]

Ans.(d) Image a wire AD added to form a closed loop DEFAD. Current flows along AD. Imagine that a wire DA is added to form a closed loop ABCDA. Current flows along DA. Effectively there is no current in DA or AB. The point (a, 0, a) lies in the x-z plane. The magnetic field due to current in ABCDA will be in positive Z- direction.
11.Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are vA and vB respectively and the trajectories are as shown in the figure. Then [2001-2 marks]

Ans.(b) Magnetic force on the charged particle provides centripetal force for circular motion of the charged particle, when the magnetic field exists perpendicular to the plane of motion.

12.A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is [2001-2 marks]

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13.A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region[JEE 2002 -2 marks]

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15.The magnetic fields lines due to a bar magnet are correctly shown in [JEE 2002 -2 marks]

Ans.(d) The magnetic field lines from closed loops. Outside magnet, they ran from N-pole to S-pole. Inside magnet, they run from S-pole to N-pole. They are not absent inside the magnet.
16.For a positively charged particle moving in a x-y plane initially along the x-axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond The curved path is shown in the x-y plane and is found to be non­circular. Which one of the following combinations is possible?[2003-2 marks]

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17.A conducting loop, carrying a current I, is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

a)contract
b)expand
c)move towards +ve x-axis.
d)move towards -ve x-axis.

Ans.(b) According to Fleming’s left hand rule, it is clear that a force acts radially outwards. The magnetic field is imposed at right angles to loop. The loop will have a tendency to expand under the force acting along outward drawn normal.
18.A current carrying loop is placed in a uniform magnetic field in four different orientations. I,II,III & IV. Arrange them in the decreasing order of potential energy. [2003-2 marks]

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22.A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown In the fig­ure. When the system is put in a uniform mag­netic field of strength B going into the plane of the paper, the wire takes the shape of a circle.The tension in the wire is.

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23.A long insulated copper wire is closely wound as a spiral of ‘N’ turns. The spiral has inner radius a and outer radius b. The spiral lies in the x-y plane and a steady current T flows through the wire. The Z-component of the magnetic field at the centre of the spiral is

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24.Which of the field patterns given below is valid for electric field as well as for magnetic field ?

Ans.(c) Induced electric field lines and magnetic field lines always form closed loop.
Multiple Choice with ONE or More Than ONE Correct answers
25.A magnetic needle is kept in a non-uniform magnetic field. It experiences [1982-3 marks]
a)a force and a torque
b)a force but not a torque
c)a torque but not a force
d)neither a force nor a torque.
Ans.(a) The magnetic needle experiences a force and a torque. The two poles of the needle will be acted upon by different forces in different directions constituting a force and a torque.
26.A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represents the electric and magnetic fields respectively, this region of space may have    [1985-2 marks]

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27.A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If steady current I is established in the wire as shown in the figure, the loop will[1985-2 marks]

a)rotate about an axis parallel to the wire
b)move away from the wire
c)move towards the wire
d)remain stationary
Ans.(c) Current / in wire and current i in AB are parallel and in same direction.AB will be attracted towards wire. Wire and CD carry parallel currnets in opposite directions. Repulsion occurs between them. The distance is more from wire and so the force of repulsion of CD will be less than the force of attraction on AB.BC and da are at right angles to wire and carry currents in opposite directions. Their net force will be zero. Due to greater attractive force on AB , the loop will move towards the wire.
28.Two thin long parallel wires seperated by a distance b are carrying a current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is [1986-2 marks]

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29.Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R1 and R2respectively. The ratio of the mass of X to that Y is[1988-2 marks]

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32.A current I flows along the length of an infinitely long, straight, thin-walled pipe. Then[1993-2 marks]
a)the magnetic field at all points inside the pipe is the same, but not zero.
b)the magnetic field at any point inside the pipe is zero
c)the magnetic field is zero only on the axis of the pipe
d)the magnetic field is different at different points inside the pipe.
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Ans.(a), (c) Magnetic force on a charged particle provides the necessary centripetal force required for circular motion of the charged particle, when a uniform magnetic field is imposed perpendicular to its velocity.
34.Two very long, straight, parallel wires carry steady currents I & -I respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires, in the plane of the wires . Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is :[1998-2 marks]

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35.A long current carrying wire, carrying current I1, such that I1 is flowing out from the plane of paper is placed at O. A steady state current I2 is flowing in the loop ABCD    [2006-5 marks]

a)the net force is zero
b)the net torque is zero
c)As seen from O, the loop will rotate in clockwise along OO1 axis
d)As seen from O, the loop will rotate in anticlockwise direction along OO axis.
Ans.(a), (c) The current carrying wire is placed at O. It carries a current l1, which flows out from the plane of paper. Field lines are circular around the wire, due to l1

36.A particle of mass m and charge q moving with velocity V enters region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the region II is /. Choose the correct choice(s).  [2008]

Ans.(a),(c), (d) The velocity of the particle is normal to the magnetic field, and the magnetic field is uniform, so the particle will follow a circular path. The radius of the circular path is

37.An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field per­pendicular to the velocity. Which of the following statement(s) is/are true ?(2011)
a)They will never come out of the magnetic field region
b)They will come out travelling along parallel paths
c)They will come out at the same time
d)They will come out a different times
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Assertion – Reasoning type
Instructions : The following question contains statement-I (assertion) and statement -2 (reason). Of these statements, mark correct choice if
a)Statements-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statements-1 and 2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase
d)Statement-1 is false, statement-2 is true.
38.Statement – 1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
Statement – 2:Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.  [2008]
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Comprehension based question
Advanced countries are making use of powerful electromagnets to move trains at very high speed. These trains are called maglev trains (abbreviated from magnetic levitation). These trains float on a guide way and do not run on steel tail tracks. Instead of using an engine based on fossil fuels, they make use of magnetic field forces. The magnetized coils are arranged in the guideway which repel the strong magnets placed in the trains’s under carriage. This helps train move over the guideway, a technic called electro dynamic suspension. When current passes in the coils of guideway, a typical magnetic field is set up between the undercarriage of train and guideway which pushes and pulls the train along the guideway depending on the requirement.The lack of friction and its aerodynamic style allows the train to move at very high speed.
39.The levitation of the train is due to
a)mechanical force [2006-5 marks]
b)electrostatic attraction
c)electrostatic repulsion’
d)magnetic repulsion
Ans.(d) The levitation of the train is due to magnetic repulsion.
40.The disadvantage of maglev trains is[2006-5 marks]
a)more friction           b) less pollution
c) less wear and tear    d) high initial cost
Ans.(d) The disadvantage of maglev trains is that initial cost is high.
41.The force which makes maglev move is[2006-5 marks]
a) gravitational      b) magnetic
c) nuclear forces     d) air drag
Ans.(b) The magnetic force will pull the vehicle.
Matching Type

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43.Two wires each carrying a steady current I are shown in four configurations in column I. Some of the resulting effects are described in column II. Match the statements in column I with the statements in column II.[2007]
Ans.The direction of magnetic field at P due to the current in inside loop is perpendicular to the plane of the loop and upwards.Due to current in outer loop, the magnetic field at P is perpendicular to the plane of loop and downwards. Since the currents are in opposite direction, the wires repel each other.
Subjective / Numerical integer type
44.A bar magnet is placed with its north pole pointing north and its south pole pointing south. Draw a figure to show the location of neutral points.[1979]
Ans.In this case, the force due to the earth’s field is in the same direction as the field of the magnet but near the neutral points lie on the line at right angles to the axis of the magnet and passing through its middle point.
45.A potential difference of 600 volt is applied across the plates of a parallel plate condenser. The separation between the plates is 3 mm. An electron projected vertically, parallel to the plates, with a velocity of 2×106m/sec moves un deflected between the plates. Find the magnitude and direction of the magnetic field in the region between the condenser plates. (Neglect the edge effects).

Ans.Since the electron moves undeflected between the plates of condenser, there should be equal and opposite magnetic and electric forces upon it. Electric force is to the left, due to positively charged plate. Magnetic force on electron should be towards right. The magnetic field should therefore be directed perpendicular to plane of paper inwards, according to Fleming’s left hand rule.Magnetic force = Electrical force

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Ans.The velocity of the charged particle is perpendicular to uniform magnetic field. The speed of the particle does not change in the field. The particle will move along a circular path. The magnetic force provides the necessary centripetal force to the particle.
In figure (a), the magnetic field is directed along the inward normal to the plane of the paper. The particle leaves the region of the field at F .
In figure (b) the direction of magnetic field is along the outward normal to the plane of the paper. The particle enters the region of the field at £. Magnetic force = Centripetal force

48.A beam of protons with a velocity 4×105m/sec enters a uniform magnetic field of 0.3 tesla at an angle of 60° to the magnetic field. Find the radius of the helical path taken by the proton beam. Also find the pitch of the helix (which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of rotation).[1986-6 marks]
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49.Two long straight parallel wires are 2 metre apart,perpendicular to the plane of the paper (see figure).The wire A carries a current of 9.6 ampere, directed into the plane of the paper. The wire B carries a current such that the magnetic field of induction at the point P, at distance of (10/11) metre from the wire B, is zero. Find   [1987-7 marks]

i)The magnitude and direction of the current in B.
ii)The magnitude of the magnetic field of induction at the point S.
iii)The force per unit length on the wire B.
Ans.The two parallel wires are perpendicular to the plane of the paper. The wire A carries current directed into the plane of the paper.
(i) Magnitude and direction of current in 5 Direction of current in g should be perpendicular to the paper outwards………….(i)

50.A pair of stationary and infinitely long bent wires are placed in the xy plane as shown in fig. The wires can currents of i=10 ampere each as shown in the figure. The segments L and M are along the x-axis.The segments P and Q are parallel to the y- axis such that OS = OR = 0.02m . Find the magnitude and direction of the magnetic induction at the origin O.     [1989-6 marks]

Ans.A pair of bent wires are placed in x — y plane. The segments p and m are along the x— axis. The segments p and Q are parallel to y — axis.

51.Two long parallel wires carrying current 2.5 ampere and I ampere in the same direction (directed into the plane of the paper) are held at P and Q respectively such that they are perpendicular to the plane of paper. The points P and Q are located at distance of 5 metre and 2 metre respectively from a collinear point R (see figure).

Ans.Two parallel wires are held at p and Q such that they are perpendicular to the plane of paper.They carry currents in the same direction, directed into the plane of the paper.

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Ans.A straight segment OC, placed along x— axis, carries a current I. Two infinitely long straight wires, A and B , carry a current I each.To obtain an expression for the force on OC:

Ans.The electron gun G shots electrons in the positive x- direction. A uniform magnetic field at 60° with x-axis, in the region outside electron gun, constrains electrons to follow a helical path and hit the spot S.The velocity of electron makes an angle of 60° with the magnetic field.

55.A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20 A, is in equilibrium at a height of 0.01 m over another parallel long wire CD which is fixed in a horizontal plane and carries a steady current of 30 A, as shown in figure.Show that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.

Ans.AB and CD are parallel wires. When they carry currents in same direction there will be attraction between them. When currents in them are in opposite directions, there will be repulsion between them. When AB is slightly depressed, force of repulsion will push it upwards and AB may vibrate. If force of attraction exists, CD will attract AB and vibration of AB will not be possible. Consequently AB and CD carry currents in opposite directions.

56.An electron in the ground state of hydrogen atom is revolving in anti clock-wise direction in a circular orbit of radius R [1996-5 marks].

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57.Three infinitely long thin wires each carrying current i in the same direction , are in the x-y plane of a gravity free space . The central wire is along the y-axis while the other two are along x = ± d. [JEE ’97, 5]
i)Find the locus of the points for which the magnetic field B is zero .
ii)If the central wire is displaced along the z-direction by a small amount & released, show that it will execute simple harmonic motion . If the linear density of the wires is 1 , find the frequency of oscillation.
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59.A uniform, constant magnetic field g is directed at an angle of 45° to the x-axis in the xy-plane, PQRS is a rigid, square wire frame carrying a steady current I0(clockwise), with its centre at the origin O. At time t = 0, the frame is at rest in the position as shown in the figure, with its sides parallel to the x & y axis. Each side of the frame is of mass M & length L [1998- 2+6 marks] a)Find the value of L if the particle emerges from the region of magnetic field with its final velocity at an angle 30° to its initial velocity.b)Find the final velocity of the particle and the time spent by it in the magnetic field, if the magnetic field now extends up to 2.1 L

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61.A circular loop of radius R is bent along a diameter and given a shape as shown in the figure. One of the semicircles (KNM) lies in the x – z plane and the other one (KLM) in the y – z plane with their centres at the origin Current I is flowing through each of the semicircles as shown in figure

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62.A current of 10A flows around a closed path in a circuit which is in the horizontal plane as shown in the figure. The circuit consists of eight alternating arcs of radii r1 = 0.08 m and r2 = 0.12 m. Each arc subtends the same angle at the centre.

a)Find the magnetic field produced by this circuit at the centre.
b)An infinitely long straight wire carrying a current of 10A is a passing through the centre of the above circuit vertically with the direction of the current being into the plane of the circuit. What is the force acting on the wire at the centre due to the current in the circuit? What is the force acting on the arc AC the straight segment CD due to the current at the centre?
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True / False type
69.No net force acts on a rectangular coil carrying a steady current when suspended freely in a uniform magnetic field.       [1981-2 marks]
Ans.True : A current carrying coil behaves like a magnetic dipole. The net force on the magnetic dipole placed in uniform magnetic field is zero.
70.There is no change in the energy of a charged particle moving in magnetic field although a magnetic force is acting on it. [1983-2 marks]
Ans.True : The magnetic force on a charged particle acts at right angles to the direction of velocity of particle . Hence the speed of the particles remains unaffected by the force. The workdone by the force is zero. Therefore the energy of moving charged particle remains unchanged.
71.A charged particle enters a region of uniform magnetic field at an angle of 85° to the magneitc line of force. The path of the particle is a circle.[1983-2 marks]
Ans.False : The charged particle moves along a circular path when it enters the magnetic field at right angles. At other angles, the path will be a helix. The particle has a circular motion as well as a linear motion to trace a helix.
72.An electron and proton are moving with the same kinetic energy along the same direction. When they pass through a uniform magnetic field perpen­dicular to the direction of their motion, they describe circular paths of the same radius.[1985-3 marks]
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Fill in the blanks type
73.A neutron, a proton, an electron and an alpha particle enter a region of constant magnetic field with equal velocities. The magnetic field is along the inward normal to the plane of the paper. The tracks of the particles are labelled in fig. The electron follows track ……………..  and the alpha particle follows track [1984-2 marks]

Ans.A neutron is electrically a neutarl particle. It goes along path C, without any deviation.According to Fleming’s left hand rule, the force on negatively charged electron will be towards right. It will follow track D. Proton and alpha particles are positively charged particles. Magnetic force on these particles will be towards left. Centripetal force = magnetic force.
74.A wire of length L metre carrying a current i ampere is bent in the form of a circle. The magnitude of its magnetic moment is…………….in MKS unit. [1987-2 marks]
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75.In a hydrogen atom, the electron moves in an orbit of radius 0.5 A making 1o16 revolutions per second. The magnetic moment associated with the orbital motion of the electron is …………………[1988-2 marks]
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76.The wire loop PQRSP formed by joining two semicircular wires of radii and R2 carries a current I as shown in the figure. The magnitude of the magnetic induction at the centre C is ………………………………..[1988-2 marks]

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77.A wire ABCDEF (with each side of length L) bent as shown in figure and carrying a current I is placed in a uniform magnetic induction B parallel to the positive y-direction. The force experienced by the wire is…………..  in the ……………direction.

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79.A uniform magnetic field with a slit system, as shown in figure, is to be used as a momentum filter for high-energy charged particles. With a field B tesla, it is found that the filter transmits a -particles each of energy 5.3 MeV. The magnetic field is increased to 2.3 B tesla and deuterons are passed into the filter. The energy of each deuteron transmitted by the filter……………………………….. [1997-1 mark]

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