Solved papers for JEE Main & Advanced Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव JEE PYQ-Magnetic Effects Of Current

done JEE PYQ-Magnetic Effects Of Current Total Questions - 90

• question_answer1) If an electron and a proton having same momenta enter perpendicularly to a magnetic field, then                              [AIEEE 2002]

A)
curved path of electron and proton will be same (ignoring the sense of revolution)

B)
they will move undeflected

C)
curved path of electron is more curved than that of proton

D)
path of proton is more curved

• question_answer2) If a current is passed through a spring, then the spring will                              [AIEEE 2002]

A)
expand

B)
compress

C)
remain same

D)
None of these

• question_answer3) The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its                                                         [AIEEE 2002]

A)
speed

B)
mass

C)
charge

D)
magnetic induction

• question_answer4) A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is [AIEEE 2003]

A)
$\left( \frac{M{{v}^{2}}}{R} \right)2\pi R$

B)
zero

C)
BQ $2\pi R$

D)
BQv $2\pi R$

• question_answer5) A particle of charge $-16\times {{10}^{-18}}C$ moving with velocity $10m{{s}^{-1}}$ along the x-axis enters a region where a magnetic field of induction B is along the y-axis and an electric field of magnitude ${{10}^{4}}$ V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is [AIEEE 2003]

A)
${{10}^{3}}$ Wb / ${{m}^{2}}$

B)
${{10}^{5}}$ Wb/${{m}^{2}}$

C)
${{10}^{16}}$ Wb/${{m}^{2}}$

D)
${{10}^{-3}}$ Wb/${{m}^{2}}$

• question_answer6) A current$i$ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is                                     [AIEEE 2004]

A)
infinite

B)
zero

C)
$\frac{{{\mu }_{0}}}{4\pi }.\frac{2i}{r}T$

D)
$\frac{2i}{r}T$

• question_answer7) A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be

A)
$nB$

B)
${{n}^{2}}B$

C)
$2nB$

D)
$2{{n}^{2}}B$

• question_answer8) The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from, the centre is 54$\mu T$. What will be its value at tile centre of the loop?                             [AIEEE 2004]

A)
$250\mu T$

B)
$150\mu T$

C)
$125\mu T$

D)
$75\mu T$

• question_answer9) Two long conductors, separated by a distance d. carry currents${{I}_{1}}$and${{I}_{2}}$in the same direction. They exert a force F on each other. Now, the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3d. The new value of the force between them is [AIEEE 2004]

A)
$-2F$

B)
$F/3$

C)
$-2F/3$

D)
$-F/3$

• question_answer10) The materials suitable for making electromagnets should have            [AIEEE 2004]

A)
high retentivity and high coercivity

B)
low retentivity and low coercivity

C)
high retentivity and low coercivity

D)
low retentivity and high coercivity

• question_answer11) Two thin, long, parallel wires, separated by a distance d carry a current of i ampere in the same direction. They will       [AIEEE 2005]

A)
attract each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}$

B)
repel each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}$

C)
attract each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}$

D)
repel each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}$

• question_answer12) Two concentric coils each of radius equal to$2\pi$cm are placed at right angles to each other. 3 A and 4 A are the currents flowing in each coil respectively. The magnetic induction in $Wb/{{m}^{2}}$at the centre   of   the   coils , will   be $({{\mu }_{0}}=4\pi \times {{10}^{-7}}Wb/Am)$            [AIEEE 2005]

A)
$12\times {{10}^{-5}}$

B)
${{10}^{-5}}$

C)
$5\times {{10}^{-5}}$

D)
$7\times {{10}^{-5}}$

• question_answer13) A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then        [AIEEE 2005]

A)
its velocity will decrease

B)
its velocity will increase

C)
it will turn towards right of direction of motion

D)
it will turn towards left of direction of motion

• question_answer14) A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is                [AIEEE 2005]

A)
$\frac{2\pi mq}{B}$

B)
$\frac{2\pi {{q}^{2}}B}{m}$

C)
$\frac{2\pi qB}{m}$

D)
$\frac{2\pi m}{qB}$

• question_answer15) In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a          [AIEEE 2006]

A)
helix

B)
straight line

C)
ellipse

D)
circle

• question_answer16) A long solenoid has 200 turns/cm and carries a current j. The magnetic field at its centre is 6.28 $\times {{10}^{-2}}Wb/{{m}^{2}}$. Another long solenoid has 100 turns/cm and it carries a current$i/3$. The value of the magnetic field at its centre is                                        [AIEEE 2006]

A)
$1.05\times {{10}^{-2}}Wb/{{m}^{2}}$

B)
$1.05\times {{10}^{-5}}Wb/{{m}^{2}}$

C)
$1.05\times {{10}^{-3}}Wb/{{m}^{2}}$

D)
$1.05\times {{10}^{-4}}Wb/{{m}^{2}}$

• question_answer17) A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at$2a/\sqrt{3}$and$2a\sqrt{3}$is                [AIEEE 2007]

A)
$a/\sqrt{3}$

B)
4

C)
1

D)
$a\sqrt{3}$

• question_answer18) A current$^{20}{{C}_{0}}{{-}^{20}}{{C}_{1}}{{+}^{20}}{{C}_{2}}{{-}^{20}}{{C}_{3}}+....{{+}^{20}}{{C}_{10}}$flows along the length of an infinitely long, straight, thin walled pipe. Then, [AIEEE 2007]

A)
The magnetic field is zero only on the axis of the pipe

B)
The magnetic field is different at different points inside the pipe

C)
The magnetic field at any point inside the pipe is zero

D)
The magnetic field at all points inside the pipe is the same, but not zero

• question_answer19) A charged particle with charge g enters a region of constant, uniform and mutually orthogonal fields E and B with a velocity v perpendicular to both E and B and comes out without any change in magnitude or direction of v. Then,                                    [AIEEE 2007]

A)
$\frac{1}{5}$

B)
$\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-....$

C)
${{e}^{-2}}$

D)
${{e}^{-1}}$

• question_answer20) A charged particle moves through a magnetic field perpendicular to its direction. Then, [AIEEE 2007]

A)
the momentum changes but the kinetic energy is constant

B)
both momentum and kinetic energy of the particle are not constant

C)
both momentum and kinetic energy of the particle are constant

D)
kinetic energy changes but the momentum is constant

• question_answer21) Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current$f(x)$and COD carries a current$x=0$. The magnetic field on a point lying at a distance d from 0, in a direction perpendicular to the plane of the wires AOB and COD, will be given by                                                       [AIEEE 2007]

A)
$f:R/\{0\}\to R$

B)
$f(x)=\frac{1}{x}-\frac{2}{{{e}^{2x}}-1}$

C)
$x=0$

D)
$x$

• question_answer22)  Directions: are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is $30{}^\text{o}.$ another straight thin wire with steady current${{I}_{1}}$flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field (2) due to the loop ABCD at the origin (O) is [AIEEE 2009]

A)
zero

B)
$\frac{{{\mu }_{0}}I(b-a)}{24ab}$

C)
$\frac{{{\mu }_{0}}I}{4\pi }\left[ \frac{b-a}{ab} \right]$

D)
$\frac{{{\mu }_{0}}I}{4\pi }\left[ 2(b\_a)+\frac{\pi }{3}(a+b) \right]$

• question_answer23)  Directions: are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is $30{}^\text{o}.$ another straight thin wire with steady current${{I}_{1}}$flowing out of the plane of the paper is kept at the origin. Due to the presence of the current ${{I}_{1}}$ at the origin:                                                [AIEEE 2009]

A)
the forces on AB and DC are zero

B)
the forces on AD and BC are zero

C)
the magnitude of the net force on the loop is given by$\frac{{{I}_{1}}I}{4\pi }{{\mu }_{0}}\left[ 2(b-a)+\frac{\pi }{3}(a+b) \right]$

D)
the magnitude of the net force on the loop is given by$\frac{{{\mu }_{0}}I{{I}_{1}}}{24ab}(b-a)$

• question_answer24) 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 is given by -            [AIEEE 2010]

A)

B)

C)

D)

• question_answer25) A current I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R. The magnitude of the magnetic induction along its axis is              [AIEEE 2011]

A)
$\frac{{{\mu }_{0}}I}{4\pi R}$

B)
$\frac{{{\mu }_{0}}I}{{{\pi }^{2}}R}$

C)
$\frac{{{\mu }_{0}}I}{2{{\pi }^{2}}R}$

D)
$\frac{{{\mu }_{0}}I}{2\pi R}$

• question_answer26) An electric charge +q moves with velocity $\vec{v}=3\hat{i}+4\hat{j}+\hat{k},$in an electromagnetic field given by: $\vec{E}=3\hat{i}+\hat{j}+2\hat{k}$and $\vec{B}=\hat{i}+\hat{j}+3\hat{k}.$The y - component of the force experienced by + q is:                            [AIEEE 11-05-2011]

A)
11q

B)
5q

C)
3q

D)
2q

• question_answer27) A thin circular disk of radius R is uniformly charged with density $\sigma >0$per unit area. The disk rotates about its axis with a uniform angular speed $\omega .$The magnetic moment of the disk is :                                         [AIEEE 11-05-2011]

A)
$\pi {{R}^{4}}\sigma \omega$

B)
$\frac{\pi {{R}^{4}}}{2}\sigma \omega$

C)
$\frac{\pi {{R}^{4}}}{4}\sigma \omega$

D)
$2\pi {{R}^{4}}\sigma \omega$

• question_answer28) Proton, Deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively ${{r}_{p}},{{r}_{d}}$ and ${{r}_{\alpha }}$. Which one of the following relation is correct? [AIEEE 2012]

A)
${{r}_{\alpha }}={{r}_{p}}={{r}_{d}}$

B)
${{r}_{\alpha }}={{r}_{p}}<{{r}_{d}}$

C)
${{r}_{\alpha }}>{{r}_{d}}>{{r}_{p}}$

D)
${{r}_{\alpha }}={{r}_{d}}>{{r}_{p}}$

• question_answer29) The velocity of certain ions that pass un deflected through crossed electric field E = 7.7 k V/m and magnetic field B = 0.14T is                                     [JEE ONLINE 07-05-2012]

A)
18km/s

B)
77km/s

C)
55km/s

D)
1078 km/s

• question_answer30) The magnetic force acting on charged particle of charge $2\mu C$in magnetic field of 2 F acting in y-direction, when the particle velocity is $\left( 2\hat{i}+3\hat{j} \right)\times {{10}^{6}}m{{s}^{-1}}$ is [JEE ONLINE 12-05-2012]

A)
8 N in z-direction

B)
8 N in y-direction

C)
4 N in y-direction

D)
4 N in z-direction

• question_answer31)  The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of 10 g and is 5 cm long. The wire is hanging as shown in the figure. The springs stretch 0.5 cm under the weight of the wire and the circuit has a, total resistance of $12\Omega .$ When the lower wire is subjected to a static magnetic field, the springs, stretch an additional 0.3 cm. The magnetic field is                                             [JEE ONLINE 12-05-2012]

A)
0.6 T and directed out of page

B)
1.2 T and directed into the plane of page

C)
0.6 T and directed into the plane of page

D)
1.2 T and directed out of page

• question_answer32) A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius R, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be                                       [JEE ONLINE 19-05-2012]

A)
$\sqrt{2}R$

B)
$\frac{R}{\sqrt{2}}$

C)
$\frac{R}{2}$

D)
R

• question_answer33)  Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. [JEE ONLINE 26-05-2012] The force acting on the conductor B, which is situated at 10 cm distance from A will be

A)
$8\times {{10}^{-5}}N$

B)
$5\times {{10}^{-5}}N$

C)
$8\pi \times {{10}^{-7}}N$

D)
$4\pi \times {{10}^{-7}}N$

• question_answer34)  This question has Statement 1 and Statement 2.                              [JEE ONLINE 26-05-2012] Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field.

A)
Statement 1 is false, Statement 2 is time.

B)
Statement 1 is time, Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.

C)
Statement 1 is true. Statement 2 is false.

D)
Statement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.

• question_answer35) An electric current is flowing through a circular coil of radius R. The ratio of the magnetic field at the centre of the centre of the coil and that at a distance $2\sqrt{2}$R from the centre the centre of the coil and its axis is:                        [JEE ONLINE 09-04-2013]

A)
$2\sqrt{2}$

B)
$27$

C)
$36$

D)
$8$

• question_answer36) Choose the correct sketch of the magnetic field lies of a circular current loop shown by the dot  and the cross $\otimes$[JEE ONLINE 22-04-2013]

A)

B)

C)

D)

• question_answer37) A current $i$ is flowing in a straight conductor of length L. The magnetic induction at a point on its axis at a distance $\frac{\operatorname{L}}{4}$  from its centre will be:                            [JEE ONLINE 22-04-2013]

A)
Zero

B)
$\frac{{{\mu }_{0}}\operatorname{i}}{2\pi L}$

C)
$\frac{{{\mu }_{0}}\operatorname{i}}{\sqrt{2L}}$

D)
$\frac{4{{\mu }_{0}}\operatorname{i}}{\sqrt{5}\,\pi L}$

• question_answer38) A particle of charge $16\times {{10}^{-16}}$ C moving with velocity  $10{{\operatorname{ms}}^{-1}}$ along $x-$ axis enters enters a region where magnetic field of induction $\overset{\to }{\mathop{\operatorname{B}}}\,$ is along the $y$-axis and an electric field of magnitude ${{10}^{4}}{{\operatorname{V}}^{-1}}$ is along the negative z-axis. If the charged particle continues moving along $x-axis$, the magnitude of magnitude of $\overset{\to }{\mathop{\operatorname{B}}}\,$is :                      [JEE ONLINE 23-04-2013]

A)
$16\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

B)
$2\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

C)
$1\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

D)
$4\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}$

• question_answer39) A parallel plate capacitor of area 60 ${{\operatorname{cm}}^{2}}$ and separation 3 mm is charged  initially to $90\mu \operatorname{C}.$ If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of $2.5\times {{10}^{-8}}\operatorname{C}/s,$ then what is the magnetic field between the plates? [JEE ONLINE 23-04-2013]

A)
$2.5\times {{10}^{-8}}\operatorname{T}$

B)
$2.0\times {{10}^{-7}}\operatorname{T}$

C)
$1.63\times {{10}^{-11}}\operatorname{T}$

D)
Zero

• question_answer40) One of the two small circular coils, (none of them having any self-inductance) is suspended with a V-shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a de supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect? [JEE ONLINE 25-04-2013]

A)
Both the same carry currents in the same direction

B)
Coils will attract each other, even if the supply is as source.

C)
Force is proportional to ${{\operatorname{d}}^{-4}}$, d = distance between the centres of the coils.

D)
Force is proportional to ${{\operatorname{d}}^{-2}}$

• question_answer41) A metal sample carrying a current along X-axis with density ${{J}_{x}}$ is subjected to a magnetic filed ${{\operatorname{B}}_{z}}$ (along-z axis). The electric field ${{\operatorname{E}}_{y}}$developed along Y-axis is directly proportional to ${{\operatorname{J}}_{x}}$ as well as ${{B}_{z}}$. The constant of proportionality as has SI unit.                          [JEE ONLINE 25-04-2013]

A)
$\frac{{{m}^{2}}}{A}$

B)
$\frac{{{m}^{3}}}{A\operatorname{s}}$

C)
$\frac{{{m}^{2}}}{A\operatorname{s}}$

D)
$\frac{{{\operatorname{A}}_{\operatorname{S}}}}{{{\operatorname{m}}^{3}}}$

• question_answer42)  A conductor lies along the z-axis at $-1.5\le z<1.5m$and carries a fixed current of 10.0 A in $-{{\hat{a}}_{z}}$direction (see figure). For a field  $\vec{B}=3.0\times {{10}^{-4}}{{e}^{-0.2x}}{{\hat{a}}_{y}}T,$ find the power required to move the conductor at constant speed to $x=2.0m,y=0m$in $5\times {{10}^{-3}}s.$ Assume parallel motion along the x-axis.                                      [JEE MAIN 2014]

A)
14.85 W

B)
29.7 W

C)
1.57 W

D)
2.97 W

• question_answer43)  Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:            [JEE ONLINE 11-04-2014]

A)
$3\times {{10}^{-4}}N$ toward right

B)
$6\times {{10}^{-4}}N$ toward right

C)
$9\times {{10}^{-4}}N$toward right

D)
Zero

• question_answer44) A positive charge 'q' of mass 'm' is moving along the + x axis. We wish to apply a uniform magnetic field B for time $\Delta t$so that the charge reverses its direction crossing the y axis at a distance d. Then:       [JEE ONLINE 12-04-2014]

A)
$B=\frac{mv}{qd}$and$\Delta t=\frac{\pi d}{v}$

B)
$B=\frac{mv}{2qd}$and$\Delta t=\frac{\pi d}{2v}$

C)
$B=\frac{2mv}{qd}$and$\Delta t=\frac{\pi d}{2v}$

D)
$B=\frac{2mv}{qd}$and$\Delta t=\frac{\pi d}{v}$

• question_answer45) Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field ${{B}_{1}},$ at its centre when a current I passes through it. The ratio ${{B}_{1}}:{{B}_{2}}$ is:          [JEE ONLINE 12-04-2014]

A)
1 : 1

B)
1 : 3

C)
1 : 9

D)
9 : 1

• question_answer46)  Two long current carrying thin wires, both with current I, and held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle $'\theta '$ with the vertical. If wires have mass $\lambda$per unit length then the value of I is:                                                       [JEE MAIN 2015] (g = gravitational acceleration)

A)
$2\sqrt{\frac{\pi gL}{{{\mu }_{0}}}\tan \theta }$

B)
$\sqrt{\frac{\pi \lambda gL}{{{\mu }_{0}}}\tan \theta }$

C)
$\sin \theta \sqrt{\frac{\pi \lambda gL}{{{\mu }_{0}}\cos \theta }}$

D)
$2\sin \theta \sqrt{\frac{\pi \lambda gL}{{{\mu }_{0}}\cos \theta }}$

• question_answer47) A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12A is placed in different orientations as shown in the figures below:                             [JEE MAIN 2015]

A)

B)

C)

D)

• question_answer48) Two coaxial solenoids of different radii carry current I in the same direction. Let ${{\vec{F}}_{1}}$be the magnetic force on the inner soleoid due to the outer one and ${{\vec{F}}_{2}}$be the magnetic force on the outer solenoid due to the inner one. Then:                                        [JEE MAIN 2015]

A)
${{\vec{F}}_{1}}$is radially inwards and ${{\vec{F}}_{2}}=0$

B)
${{\vec{F}}_{1}}$is radially outwards and ${{\vec{F}}_{2}}=0$

C)
${{\vec{F}}_{1}}={{\vec{F}}_{2}}=0$

D)
${{\vec{F}}_{1}}$is radially inwards and ${{\vec{F}}_{2}}$is radially onwards

• question_answer49)  A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width 'd. If $'\alpha '$ be the angle of deviation of proton from initial direction of motion (see figure), the value of sin a will be:            [JEE ONLINE 10-04-2015]

A)
${{q}^{V}}\sqrt{\frac{Bd}{2m}}$

B)
$Bd\sqrt{\frac{q}{2mV}}$

C)
$\frac{B}{2}\sqrt{\frac{qd}{mV}}$

D)
$\frac{B}{d}\sqrt{\frac{q}{2mV}}$

• question_answer50) If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth  level will be:                        [JEE ONLINE 10-04-2015]

A)
$n\left( \frac{hqB}{2\pi m} \right)$

B)
$n\left( \frac{hqB}{8\pi m} \right)$

C)
$n\left( \frac{hqB}{4\pi m} \right)$

D)
$n\left( \frac{hqB}{\pi m} \right)$

• question_answer51) Two long straight parallel wires, carrying (adjustable) currents $\,{{I}_{1}}$and $\,{{I}_{2}},$ are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F', on the product $\,{{I}_{1}}\,{{I}_{2}},$would be :             [JEE MAIN 11-04-2015]

A)

B)

C)

D)

• question_answer52)  A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle $2{{\theta }_{0}}$ at the centre of the circle (of which it forms an arch) then the tension in the wire is :                                                  [JEE MAIN 11-04-2015]

A)
$IBR$

B)
$\frac{IBR}{\sin {{\theta }_{0}}}$

C)
$\frac{IBR}{2\sin {{\theta }_{0}}}$

D)
$\frac{IBR{{\theta }_{0}}}{\sin {{\theta }_{0}}}$

• question_answer53) Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If ${{B}_{A}}$and ${{B}_{B}}$are the values of magnetic field at the centres of the circle and square respectively, then the ratio $\frac{{{B}_{A}}}{{{B}_{B}}}$is:      [JEE MAIN - I 3-4-2016]

A)
$\frac{{{\pi }^{2}}}{8\sqrt{2}}$

B)
$\frac{{{\pi }^{2}}}{8}$

C)
$\frac{{{\pi }^{2}}}{16\sqrt{2}}$

D)
$\frac{{{\pi }^{2}}}{16}$

• question_answer54) A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? [JEE Main 2017]

A)

B)

C)

D)

• question_answer55) In a certain region static electric and magentic fields exist. The magnetic field is given by $\vec{B}={{B}_{0}}\left( \hat{i}+2\hat{j}-4\hat{k} \right).$If a test charge moving with a velocity $\vec{\upsilon }={{\upsilon }_{0}}\left( 3\hat{i}-\hat{j}+2\hat{k} \right)$experience no force in that region, then the electric field in the region, in SI units, is - [JEE Online 08-04-2017]

A)
$\vec{E}=-{{\upsilon }_{0}}{{B}_{0}}\left( \hat{i}+\hat{j}+7\hat{k} \right)$

B)
$\vec{E}=-{{\upsilon }_{0}}{{B}_{0}}\left( 3\hat{i}-2\hat{j}-4\hat{k} \right)$

C)
$\vec{E}={{\upsilon }_{0}}{{B}_{0}}\left( 14\hat{i}+7\hat{k} \right)$

D)
$\vec{E}={{\upsilon }_{0}}{{B}_{0}}\left( 14\hat{j}+7\hat{k} \right)$

• question_answer56) A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is -    [JEE Online 09-04-2017]

A)
away from the wire

B)
towards the wire

C)
parallel to the wire along the current

D)
parallel to the wire opposite to the current

• question_answer57) A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop $(abcd)$ of sides $10\,cm\,\times 5\,cm$ carries a current $I$ of 12 A. Out of the following different orientations which one corresponds to stable equilibrium?                  [JEE Online 09-04-2017]

A)

B)

C)

D)

• question_answer58)  An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii ${{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}$ respectively in a uniform magnetic field B. The relation between ${{r}_{e}},\,\,{{r}_{p}},\,\,{{r}_{\alpha }}$ is: [JEE Main Online 08-04-2018]

A)
${{r}_{e}}<{{r}_{p}}<{{r}_{\alpha }}$

B)
${{r}_{e}}<{{r}_{\alpha }}<{{r}_{p}}$

C)
${{r}_{e}}>{{r}_{p}}={{r}_{\alpha }}$

D)
${{r}_{e}}<{{r}_{p}}={{r}_{\alpha }}$

• question_answer59) The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is ${{B}_{1}}$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is ${{B}_{2}}.$ The ratio $\frac{{{B}_{1}}}{{{B}_{2}}}$ is: [JEE Main Online 08-04-2018]

A)
$\sqrt{2}$

B)
$\frac{1}{\sqrt{2}}$

C)
2

D)
$\sqrt{3}$

• question_answer60)  A Helmholtz coil has pair of loops, each with $N$ turns and radius$R$. They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of magnetic field at $P$, midway between the centres $A$and $C$, is given by (Refer to figure): [JEE Online 15-04-2018]

A)
$\frac{4N{{\mu }_{0}}I}{{{5}^{3/2}}R}$

B)
$\frac{8N{{\mu }_{0}}I}{{{5}^{3/2}}R}$

C)
$\frac{4N{{\mu }_{0}}I}{{{5}^{1/2}}R}$

D)
$\frac{8N{{\mu }_{0}}I}{{{5}^{1/2}}R}$

• question_answer61) A current of $1A$ is flowing on the sides of an equilateral triangle of side$4.5\times {{10}^{-2}}m$. The magnetic field at the centre of the triangle will be:                    [JEE Online 15-04-2018 (II)]

A)
$4\times {{10}^{-5}}Wb/{{m}^{2}}$

B)
Zero

C)
$2\times {{10}^{-5}}Wb/{{m}^{2}}$

D)
$8\times {{10}^{-5}}Wb/{{m}^{2}}$

• question_answer62)  A copper rod of mass $m$ slides under gravity on two smooth parallel rails, with separation 1 and set at an angle of $\theta$ with the horizontal. At the bottom, rails are joined by a resistance$R$. .There is a uniform magnetic field $B$ normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is:                         [JEE Online 15-04-2018 (II)]

A)
$\frac{mgR\cos \theta }{{{B}^{2}}{{l}^{2}}}$

B)
$\frac{mgR\sin \theta }{{{B}^{2}}{{l}^{2}}}$

C)
$\frac{mgR\tan \theta }{{{B}^{2}}{{l}^{2}}}$

D)
$\frac{mgR\cot \theta }{{{B}^{2}}{{l}^{2}}}$

• question_answer63) A charge is spread uniformly over an insulated loop of radius. If it is rotated with an angular velocity$\omega$ with respect to normal axis then the magnetic moment of the loop is [JEE Main Online 16-4-2018]

A)
$A\frac{1}{2}q\omega {{r}^{2}}$

B)
$\frac{4}{3}q\omega {{r}^{2}}$

C)
$\frac{3}{2}q\omega {{r}^{2}}$

D)
$q\omega {{r}^{2}}$

• question_answer64)  A current loop, having two circular arcs joined by two radial lines y shown in the figure. It carries a current of 10 A. The magnetic field at point 0 will be close to:                                        [JEE Main 09-Jan-2019 Morning]

A)
$~1.5\,\,\times \,\,\text{1}{{0}^{-5}}\,T$

B)
$1.0\times {{10}^{-\,5}}\,T$

C)
$1.5\,\,\times \,\,{{10}^{-7}}\,T~$

D)
$1.0\times \text{1}{{0}^{-7}}\,T$

• question_answer65) One of the two identical conducting wires of length L is bent in the form of a circular   loop and the other one into a circular coil. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $({{B}_{L}}),\,\,\,\,i.e.\,\,\,\frac{{{B}_{L}}}{{{B}_{C}}}$will be: [JEE Main 09-Jan-2019 Evening]

A)
$\frac{1}{N}$

B)
N

C)
${{N}^{2}}$

D)
$\frac{1}{{{N}^{2}}}$

• question_answer66) There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii ${{r}_{1}}$ and ${{r}_{2}}$and number of turns per unit length ${{n}_{1}}$ and ${{n}_{2}}$ respectively. The ratio of mutual inductance to the self inductance of the inner- coil is-         [JEE Main 11-Jan-2019 Morning]

A)
$\frac{{{n}_{2}}}{{{n}_{1}}}$

B)
$\frac{{{n}_{2}}}{{{n}_{1}}}.\frac{r_{2}^{2}}{r_{1}^{2}}$

C)
$\frac{{{n}_{2}}}{{{n}_{1}}}.\frac{{{r}_{1}}}{{{r}_{2}}}$

D)
$\frac{{{n}_{1}}}{{{n}_{2}}}$

• question_answer67) A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil [JEE Main 11-Jan-2019 Evening]

A)
increases by a factor of 27

B)
decreases by a factor of $9\sqrt{3}$

C)
increases by a factor of 3

D)
decreases by a factor of 9

• question_answer68) A galvanometer having a resistance of $20\,\Omega$and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is- [JEE Main 11-Jan-2019 Evening]

A)
$80\,\Omega$

B)
$125\,\Omega$

C)
$120\,\Omega$

D)
$100\,\Omega$

• question_answer69) A proton and an $\alpha -$particle (with their masses in the ratio 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform, magnetic field is set up perpendicular to their' velocities, the ratio  of the radii ${{r}_{p}}:{{r}_{\alpha }}$of the circular paths described by them will be- [JEE Main 12-Jan-2019 Morning]

A)
$1:3$

B)
$1:\sqrt{2}$

C)
$1:2$

D)
$1:\sqrt{3}$

• question_answer70) A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 m ${{s}^{-1}}$, at right angles to the horizontal component of the earths magnetic field of $0.3\times {{10}^{-4}}Wb/{{m}^{2}}.$ The value of the induced emf in wire is-  [JEE Main 12-Jan-2019 Evening]

A)
$0.3\times {{10}^{-3}}V$

B)
$2.5\times {{10}^{-3}}V$

C)
$1.5\times {{10}^{-3}}V$

D)
$1.1\times {{10}^{-3}}V$

• question_answer71) A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field $B\hat{i}$. The torque on the coil due to the magnetic field is:      [JEE Main 8-4-2019 Morning]

A)
$B\pi {{r}^{2}}IN$

B)
$\frac{B{{r}^{2}}I}{\pi N}$

C)
Zero

D)
$\frac{B\pi {{r}^{2}}I}{N}$

• question_answer72)  Two very long, straight, and insulated wires are kept at $90{}^\circ$ angle from each other in xy-plane as shown in the figure. These wires carry currents of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be :        [JEE Main 8-4-2019 Afternoon]

A)
Zero

B)
$\frac{+{{\mu }_{0}}I}{\pi d}(\hat{z})$

C)
$-\frac{{{\mu }_{0}}I}{2\pi d}(\hat{x}+\hat{y})$

D)
$\frac{{{\mu }_{0}}I}{2\pi d}(\hat{x}+\hat{y})$

• question_answer73) A moving coil galvanometer has resistance $50\Omega$and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a $5k\Omega$resistance. The maximum voltage, that can be measured using this voltmeter, will be close to:                  [JEE Main 9-4-2019 Morning]

A)
10 V

B)
20 V

C)
40 V

D)
15 V

• question_answer74)  A rigid square loop of side 'a' and carrying current ${{I}_{2}}$is lying on a horizontal surface near a long current ${{I}_{1}}$carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be : [JEE Main 9-4-2019 Morning]

A)
Attractive and equal to $\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}}{3\pi }$

B)
Repulsive and equal to $\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}}{4\pi }$

C)
Repulsive and equal to$\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}}{2\pi }$

D)
Zero

• question_answer75) A rectangular coil (Dimension $5cm\times 2.5cm)$ with 100 turns, carrying a current of 3 A in the clock-wise direction is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through$45{}^\circ$about Z-axis, then the torque on the coil is : [JEE Main 9-4-2019 Morning]

A)
0.55 Nm

B)
0.27 Nm

C)
0.38 Nm

D)
0.42 Nm

• question_answer76) The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 - 0.5 A? [JEE Main 9-4-2019 Afternoon]

A)
0.2 ohm

B)
0.002 ohm

C)
0.02 ohm

D)
0.5 ohm

• question_answer77) A very long solenoid of radius R is carrying current $I(t)=kt{{e}^{-\alpha t}}(k>0),$as a function of time $(t\ge 0).$counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by :-    [JEE Main 9-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer78)  Two wires A & B are carrying currents ${{I}_{1}}\And {{I}_{2}}$as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are: [JEE Main 10-4-2019 Morning]

A)
$x=\left( \frac{{{I}_{1}}}{{{I}_{1}}-{{I}_{2}}} \right)d$and$x=\frac{{{I}_{2}}}{({{I}_{1}}+{{I}_{2}})}d$

B)
$x=\pm \frac{{{I}_{1}}d}{({{I}_{1}}-{{I}_{2}})}$

C)
$x=\left( \frac{{{I}_{1}}}{{{I}_{1}}+{{I}_{2}}} \right)d$and$x=\frac{{{I}_{2}}}{({{I}_{1}}-{{I}_{2}})}d$

D)
$x=\left( \frac{{{I}_{2}}}{{{I}_{1}}+{{I}_{2}}} \right)d$and$x=\left( \frac{{{I}_{2}}}{{{I}_{1}}-{{I}_{2}}} \right)d$

• question_answer79) A moving coil galvanometer allows a full scale current of ${{10}^{-4}}A$. A series resistance of $2M\Omega$ is required to convert the above galvanometer into a voltmeter of range 0-5 V. Therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0-10 mA is :          [JEE Main 10-4-2019 Morning]

A)
$200\,\Omega$

B)
$100\,\Omega$

C)
$10\,\Omega$

D)
None of these

• question_answer80) The magnitude of the magnetic field at the center of an equilateral triangular loop of side 1m which is carrying a current of 10 A is : $[\text{Take}\,{{\mu }_{0}}=4\pi \times {{10}^{-7}}N{{A}^{-2}}]$ [JEE Main 10-4-2019 Afternoon]

A)
$18\mu T$

B)
$3\mu T$

C)
$1\mu T$

D)
$9\mu T$

• question_answer81) A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be : [JEE Main 10-4-2019 Afternoon]

A)
$\frac{3m}{\pi }$

B)
$\frac{4m}{\pi }$

C)
$\frac{2m}{\pi }$

D)
$\frac{m}{\pi }$

• question_answer82) A galvanometer of resistance $100\Omega$has 50 divisions on its scale and has sensitivity of $20\mu A/$division. It is to be converted to a voltmeter with three ranges, of 0-2 V, 0-10 V and 0-20 V. The appropriate circuit to do so is : [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer83) A moving coil galvanometer, having a resistance G, produces full scale deflection when a current ${{I}_{g}}$flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to ${{I}_{0}}({{I}_{0}}>{{I}_{g}})$by connecting a shunt resistance ${{R}_{A}}$ to it and (ii) into a voltmeter of range 0 to $V(V=G{{I}_{0}})$ by connecting a series resistance ${{R}_{V}}$to it. Then, [JEE Main 12-4-2019 Afternoon]

A)
${{R}_{A}}{{R}_{V}}={{G}^{2}}\left( \frac{{{I}_{g}}}{{{I}_{0}}-{{I}_{g}}} \right)$and$\frac{{{R}_{A}}}{{{R}_{V}}}={{\left( \frac{{{I}_{0}}-{{I}_{g}}}{{{I}_{g}}} \right)}^{2}}$

B)
${{R}_{A}}{{R}_{V}}={{G}^{2}}$and$\frac{{{R}_{A}}}{{{R}_{V}}}={{\left( \frac{{{I}_{g}}}{{{I}_{0}}-{{I}_{g}}} \right)}^{2}}$

C)
${{R}_{A}}{{R}_{V}}={{G}^{2}}$and$\frac{{{R}_{A}}}{{{R}_{V}}}=\frac{{{I}_{g}}}{({{I}_{g}}-{{I}_{g}})}$

D)
${{R}_{A}}{{R}_{V}}={{G}^{2}}\left( \frac{{{I}_{0}}-{{I}_{g}}}{{{I}_{g}}} \right)$and$\frac{{{R}_{A}}}{{{R}_{V}}}={{\left( \frac{{{I}_{g}}}{{{I}_{0}}-{{I}_{g}}} \right)}^{2}}$

• question_answer84)  Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) [JEE Main 12-4-2019 Afternoon]

A)
$3.0\times {{10}^{5}}T$

B)
$2.5\times {{10}^{5}}T$

C)
$2.0\times {{10}^{5}}T$

D)
$1.5\times {{10}^{5}}T$

• question_answer85) Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of ${{10}^{12}}m/{{s}^{2}}$ by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is$1.6\times {{10}^{27}}kg$) [JEE MAIN Held On 08-01-2020 Morning]

A)
$0.071\text{ }mT$

B)
$0.71\text{ }mT$

C)
$71\text{ }mT$

D)
$7.1\text{ }mT$

• question_answer86)  A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turm DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic field at the centre of circle is [JEE MAIN Held on 08-01-2020 Evening]

A)
$\frac{{{\mu }_{0}}I}{2\pi R}\left( \pi +1 \right)$

B)
$\frac{{{\mu }_{0}}I}{2R}$

C)
$\frac{{{\mu }_{0}}I}{2\pi R}\left( \pi +\frac{1}{\sqrt{2}} \right)$

D)
$\frac{{{\mu }_{0}}I}{2\pi R}\left( \pi -\frac{1}{\sqrt{2}} \right)$

• question_answer87)  A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field $E\hat{i}$and a uniform magnetic field $B\hat{k}$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $v\vec{i}$and$-2v\hat{j}$. Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale) A. $E=\frac{3}{4}\left( \frac{m{{v}^{2}}}{qa} \right)$ B. Rate of work done by the electric field at P is $\frac{3}{4}\left( \frac{m{{v}^{3}}}{a} \right)$ C. Rate of work done by both the fields at Q is zero D. The difference between the magnitude of angular momentum of the particle at P and Q is 2 mav. [JEE MAIN Held on 09-01-2020 Morning]

A)
A, B, C

B)
A, C, D

C)
A, B, C, D

D)
B, C, D

• question_answer88) A long straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and 2a, respectively from the axis of the wire is [JEE MAIN Held on 09-01-2020 Morning]

A)
$\frac{1}{2}$

B)
$\frac{3}{2}$

C)
2

D)
$\frac{2}{3}$

• question_answer89) A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period T. If the mass of the loop is m then : [JEE MAIN Held on 09-01-2020 Evening]

A)
$T=\sqrt{\frac{2\pi m}{IB}}$

B)
$T=\sqrt{\frac{\pi m}{IB}}$

C)
$T=\sqrt{\frac{2m}{IB}}$

D)
$T=\sqrt{\frac{\pi m}{2IB}}$

• question_answer90)  An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current l. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maxium possible value of v is (all symboils have their standard meaning) [JEE MAIN Held on 09-01-2020 Evening]

A)
$\frac{2e{{\mu }_{0}}nIR}{m}$

B)
$\frac{e{{\mu }_{0}}nIR}{m}$

C)
$\frac{e{{\mu }_{0}}nIR}{2m}$

D)
$\frac{e{{\mu }_{0}}nIR}{4m}$