Solved papers for JEE Main & Advanced Physics Electro Magnetic Induction JEE PYQ-Electro Magnetic Induction

done JEE PYQ-Electro Magnetic Induction Total Questions - 69

• question_answer1)  The inductance between A and D is                                                    [AIEEE 2002]

A)
$3.66$ H

B)
9 H

C)
$0.66$ H

D)
1 H

• question_answer2) If in a circular coil A of radius R, current j is flowing and in another coil B of radius 2 R, a current 2 i is flowing, then the ratio of the magnetic fields, ${{B}_{A}}$ and ${{B}_{B}}$ produced by them will be    [AIEEE 2002]

A)
1

B)
2

C)
$1/2$

D)
4

• question_answer3) In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4 A, then that in the secondary is                 [AIEEE 2002]

A)
4 A

B)
2 A

C)
6 A

D)
10 A

• question_answer4)  Wires 1 and 2 carrying currents, ${{i}_{1}}$ and ${{i}_{2}}$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance r from wire 1 (as shown in figure) due to the magnetic field of wire I?                                          [AIEEE 2002]

A)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\tan \theta$

B)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\sin \theta$

C)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\cos \theta$

D)
$\frac{{{\mu }_{0}}}{4\pi r}\,{{i}_{1}}{{i}_{2}}\,dl\,\sin \,\theta$

• question_answer5)  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 B constant in time and space, pointing perpendicular and into the plane at the loop exist everywhere with half the loop outside the field, as shown in figure. The induced emf is                     [AIEEE 2002]

A)
zero

B)
RvB

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

D)
vBL

• question_answer6) Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon                                   [AIEEE 2003]

A)
the rates at which currents are changing in the two coils

B)
relative position and orientation of the two coils

C)
time for which current is flown

D)
the currents in the two coils

• question_answer7) When the current changes from $+2$ A to $-2$ A in $0.05$ s, an emf of 8 V is induced in a coil. The coefficient of self-induction of the coil is [AIEEE 2003]

A)
$0.2$ H

B)
$0.4$ H

C)
$0.8$ H

D)
$0.1$ H

• question_answer8) A coil having n turns and resistance$R\,\Omega$. is connected with a galvanometer of resistance$4R\,\Omega$. This combination is moved in time t seconds from a magnetic field${{W}_{1}}$weber to${{W}_{2}}$ weber. The induced current in the circuit is                                         [AIEEE 2004]

A)
$\frac{{{W}_{2}}-{{W}_{1}}}{5Rnt}$

B)
$-\frac{n({{W}_{2}}-{{W}_{1}})}{5Rt}$

C)
$-\frac{({{W}_{2}}-{{W}_{1}})}{Rnt}$

D)
$-\frac{n({{W}_{2}}-{{W}_{1}})}{Rt}$

• question_answer9) In a uniform magnetic field of induction B, a wire in the form of semi-circle, of radius r rotates about the diameter of the circle with angular frequency$\omega$. If the total resistance of the circuit is R, the mean power generated per period of rotation is                       [AIEEE 2004]

A)
$\frac{B\pi {{r}^{2}}\omega }{2R}$

B)
$\frac{{{(B\pi {{r}^{2}}\omega )}^{2}}}{8R}$

C)
$\frac{{{(B\pi r\omega )}^{2}}}{2R}$

D)
$\frac{{{(B\pi r{{\omega }^{2}})}^{2}}}{8R}$

• question_answer10) A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 rad/s. If the horizontal component of the earth's magnetic field is$0.2\times {{10}^{-4}}T$then the emf developed between the two ends of the conductor is                       [AIEEE 2004]

A)
$5\mu V$

B)
$50\mu V$

C)
$5mV$

D)
$50\,mV$

• question_answer11)  One conducting 17-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v, then the emf induced in the circuit in terms of B, 1 and v, where 1 is the width of each tube, will be                                      [AIEEE 2005]

A)
$BIl$

B)
$-BIl$

C)
zero

D)
$2\,BIl$

• question_answer12) A coil of inductance 300 mH and resistance$2\Omega$. are connected to a source of voltage 2V. The current reaches half of its steady state value in                                    [AIEEE 2005]

A)
0.05s

B)
0.1s

C)
0.15s

D)
0.3s

• question_answer13) The flux linked with a coil at any instant t is given by$\phi =10{{t}^{2}}-50t+250$ The induced emf at$t=3\text{ }s$is    [AIEEE 2006]

A)
$-190V$

B)
$-10V$

C)
$10V$

D)
$190V$

• question_answer14)  An inductor$(L=100mH)$, a resistor$(R=100\,\Omega )$ and a battery$(E=100\,V)$are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is             [AIEEE 2006]

A)
$1/e\,A$

B)
$e\text{ }A$

C)
$0.1A$

D)
$1\,A$

• question_answer15) An ideal coil of 10 H is connected in series with a resistance of$\frac{1}{\sqrt{2}}$and a battery of 5 V. After 2 s, the connection is made, the current flowing (in ampere) in the circuit is [AIEEE 2007]

A)
$\sqrt{2}$

B)
e

C)
$60{}^\circ$

D)
$30{}^\circ$

• question_answer16) A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is $({{\mu }_{0}}=4\pi \times {{10}^{-7}}T\,m\,{{A}^{-1}})$                                                                    [AIEEE 2008]

A)
$5\times {{10}^{-6}}T$ southward

B)
$2.5\times {{10}^{-7}}T$ northward

C)
$2.5\times {{10}^{-7}}T$ southward

D)
$5\times {{10}^{-6}}T$ northward

• question_answer17) Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 $c{{m}^{2}}$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is $({{\mu }_{0}}=4\pi \times {{10}^{-7}}T\,m\,{{A}^{-1}})$                  [AIEEE 2008]

A)
$4.8\,\,\pi \times {{10}^{-5}}H$

B)
$2.4\,\,\pi \times {{10}^{-4}}H$

C)
$2.4\,\,\pi \times {{10}^{-5}}H$

D)
$4.8\,\,\pi \times {{10}^{-4}}H$

• question_answer18)  An inductor of inductance $L=400\text{ }mH$and resistors of resistances ${{R}_{1}}=2\text{ }\Omega$ and ${{R}_{2}}=2\Omega$ are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is:           [AIEEE 2009]

A)
$6\text{ }{{e}^{5t}}V$

B)
$\frac{12}{t}{{e}^{-3t}}V$

C)
$6\left( 1-{{e}^{\frac{-t}{0.2}}} \right)V$

D)
$12{{e}^{-5t}}V$

• question_answer19)  In the circuit shown below, the key K is closed at$t=0.$the current through the battery is -[AIEEE 2010]

A)
$\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}$at $t=0$and $\frac{V}{{{R}_{2}}}$at$t=\infty$

B)
$\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}$at $t=0$and $\frac{V}{{{R}_{2}}}$at $t=\infty$

C)
$\frac{V}{{{R}_{2}}}$at$t=0$and $\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}$at$t=\infty$

D)
$\frac{V}{{{R}_{2}}}$at $t=0$and $\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}$at$t=\infty$

• question_answer20)  A rectangular loop has a sliding connector PQ of length$l$and resistance$R\,\Omega$and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents${{I}_{1}},{{I}_{2}}$and I are -                            [AIEEE 2010]

A)
${{I}_{1}}={{I}_{2}}=\frac{B/v}{6R},I=\frac{B/v}{3R}$

B)
${{I}_{1}}=-{{I}_{2}}=\frac{B/v}{R},I=\frac{2B/v}{3R}$

C)
${{I}_{1}}={{I}_{2}}=\frac{B/v}{3R},I=\frac{2B/v}{3R}$

D)
${{I}_{1}}={{I}_{2}}=I=\frac{B/v}{R}$

• question_answer21) A boat is moving due east in a region where the earth's magnetic field is $5.0\times {{10}^{-5}}N{{A}^{-1}}$ due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is $1.50\,m{{s}^{-1}}$, the magnitude of the induced emf in the wire of aerial is                                                      [AIEEE 2011]

A)
$0.15$ mV

B)
1 mV

C)
$0.75$ mV

D)
$0.50$ mV

• question_answer22) A horizontal straight wire 20 m long extanding from to east to west falling with a speed of 5.0 M\s, at right angles to the horizontal component of the earth's magnetic field $0.30\times {{10}^{-4}}Wb/{{m}^{2}}.$The instantaneous Value of the e.m. f. induced in the wire will be :                                    [AIEEE 11-05-2011]

A)
3 mV

B)
4.5 mV

C)
1.5 mV

D)
6.0m V

• question_answer23) A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to: [AIEEE 2012]

A)
developement of air current when the plate is placed.

B)
induction of electrical charge on the plate

C)
shielding of magnetic lines of force as aluminium is a paramagnetic material.

D)
Electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.

• question_answer24) A charge Q is uniformly distributed over the surface of non-condcting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity$\omega$. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. if we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure: [AIEEE 2012]

A)

B)

C)

D)

• question_answer25)  This question has Statement 1 and Statement 2.                              [JEE ONLINE 07-05-2012] Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: The possibility of an electric bulb fusing is higher at the time of switching ON. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.

A)
Statement 1 is true. Statement 2 is false

B)
Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

C)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

D)
Statement 1 is false, Statement 2 is true.

• question_answer26)  Magnetic flux through a coil of resistance $10\Omega$is changed by $\Delta \phi$in 0.1 s. The resulting current in the coil varies with time as shown in the figure.                [JEE ONLINE 12-05-2012] Then$|\Delta \phi |$is equal to (in weber)

A)
6

B)
4

C)
2

D)
8

• question_answer27)  A coil of self-inductance L is connected at one end of two rails as shown in figure. A connector of length l, mass m can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction B going into the page. At an instant t = 0 an initial velocity Vg is imparted to it and as a result of that it starts moving along x-axis. The displacement of the connector is represented by the figure. [JEE ONLINE 19-05-2012]

A)

B)

C)

D)

• question_answer28)  This question has Statement 1 and Statement 2.                              [JEE ONLINE 19-05-2012] Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Self-inductance of a long solenoid of length L, total number of turns N and radius r is less than $\frac{\pi {{\mu }_{0}}{{N}^{2}}{{r}^{2}}}{L}.$ Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current I is $\frac{{{\mu }_{0}}NI}{L}$in the middle of the solenoid but becomes less as we move towards its ends.

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

B)
Statement 1 is true, Statement 2 is true, and Statement 2 is the correct explanation of Statement 1.

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

D)
Statement 1 is true. Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

• question_answer29) A generator has armature resistance of $0.1\Omega$and develops an induced emf of 120 F when driven at its rated speed. Its terminal voltage when a current of 50 A is being drawn is [JEE ONLINE 19-05-2012]

A)
120 V

B)
5V

C)
115 V

D)
70 V

• question_answer30)  A metallic rod of length$\ell$ is tied to a string of length$2\ell$and made to rotate with angular speed$\omega$on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is: [JEE MAIN 2013]

A)
$\frac{2B\omega {{\ell }^{2}}}{2}$

B)
$\frac{3B\omega {{\ell }^{2}}}{2}$

C)
$\frac{4B\omega {{\ell }^{2}}}{2}$

D)
$\frac{5B\omega {{\ell }^{2}}}{2}$

• question_answer31)  In an LCR circuit as shown below both switches are open initially. Now switch${{S}_{1}}$is closed,${{S}_{2}}$kept open. (q is charge on the capacitor and$\tau =RC$is Capacitive time constant). Which of the following statement is correct?                         [JEE MAIN 2013]

A)
Work done by the battery is half of the energy dissipated in the resistor

B)
$At\text{ }t=\tau ,\text{ }q=CV/2$

C)
$~At\text{ }t=2\tau ,\text{ }q=CV(1-{{e}^{-2}})$

D)
$At\text{ }t=\frac{\tau }{2},q=CV(1-{{e}^{-1}})$

• question_answer32) A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is: [JEE MAIN 2013]

A)
$9.1\times {{10}^{-11}}weber$

B)
$6\times {{10}^{-11}}weber$

C)
$3.3\times {{10}^{-11}}weber$

D)
$6.6\times {{10}^{-9}}weber$

• question_answer33)  Two coils, X and Y, are kept in close vicinity of each other. When a varying current, I(t),flows through coil X the induced emf (V (t)) in coil Y, varies in the manner shown here. The variation of I(t), with time, can then be represented by the represented by the graph labeled  as graph:[JEE ONLINE 09-04-2013] [a]                [b] [c]               [d]

A)
A

B)
C

C)
B

D)
D

• question_answer34)  A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic field $\overset{\to }{\mathop{\operatorname{B}}}\,$ pointing out of the plane of the paper. A clockwise current is set up such that i > mg/Ba, where a is the width of the loop. Then:                               [JEE ONLINE 23-04-2013]

A)
The weight rises due to a vertical force caused by the magnetic field and work is done on the system.

B)
The weight do not rise due to vertical for caused by the magnetic field and work is done on the system.

C)
The weight rises due to a vertical force caused by the magnetic field but no work is done on the system.

D)
The weight rises due to a vertical force caused by the magnetic field and work is extracted from the magnetic field.

• question_answer35)  In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to:[JEE MAIN 2014]

A)
−1

B)
$\frac{1-e}{e}$

C)
$\frac{e}{1-e}$

D)
1

• question_answer36) A coil of circular cross-section having 1000 turns and $4c{{m}^{2}}$face area is placed with its axis parallel to a magnetic field which decreases by 10-2 Wb m-2 in 0.01 s. The e.m.f. induced in the coil is:          [JEE ONLINE 11-04-2014]

A)
400 mV

B)
200 mV

C)
4 mV

D)
0.4 mV

• question_answer37) A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is:                                                    [JEE ONLINE 12-04-2014]

A)
10 cos (500 t)

B)
- 10 cos (500t)

C)
10 sin (500t)

D)
- 10 sin (500t)

• question_answer38)  A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plate of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10m{{s}^{-1}}$ (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is:  [JEE ONLINE 19-04-2014]

A)
2 mV

B)
1 mV

C)
0.75 mV

D)
0.5 mV

• question_answer39)  Figure shows a circular area of radius R where a uniform magnetic field $\vec{B}$is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?                              [JEE ONLINE 19-04-2014]

A)

B)

C)

D)
None of these

• question_answer40) An inductor (L = 0.03 H) and a resistor $(R=0.15k\Omega )$are connected in series to a battery of 15V EMF in a circuit shown below. The key ${{K}_{1}}$ has been kept closed for a long time. Then at $t=0,{{K}_{1}}$is opened and key ${{K}_{2}}$ is closed simultaneously. At t = 1ms, the current in the circuit will be : $\left( {{e}^{5}}\cong 150 \right)$                                  [JEE MAIN 2015]

A)
6.7 mA

B)
0.67 mA

C)
100 mA

D)
67 mA

• question_answer41)  An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to ${{Q}_{0}}$and then connected to the L and R as shown below: If a student plots graphs of the square of maximum charge $\left( Q_{Max}^{2} \right)$on the capacitor with time (t) for two different values ${{L}_{1}}$ and ${{L}_{2}}$ $\left( {{L}_{1}}>{{L}_{2}} \right)$of L then which of the following represents this graph correctly? (plots are schematic and not drawn of scale)                                                       [JEE MAIN 2015]

A)

B)

C)

D)

• question_answer42) When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self-inductance of the coils is:                       [JEE ONLINE 10-04-2015]

A)
3H

B)
1.67 H

C)
6 H

D)
0.67 H

• question_answer43)  In the circuits and switches ${{S}_{1}}$ and ${{S}_{2}}$ are closed at t = 0 and are kept closed for a long time. The variation of currents in the two circuits for $t\ge 0$ are roughly shown by (figures are schematic and not drawn to scale):                         [JEE ONLINE 10-04-2015]

A)

B)

C)

D)

• question_answer44) A series LR circuit is connected to a voltage source with $V(t)={{V}_{0}}\sin \Omega t.$After very large time current I (t) behaves as $\left( {{t}_{0}}>>\frac{L}{r} \right):$                                       [JEE ONLINE 09-04-2016]

A)

B)

C)

D)

• question_answer45) A conducting metal circular -wire loop of radius r is placed perpendicular to a magnetic field which varies with time as $B={{B}_{0e}}^{-t/\tau }$, where B0 and $\tau$ are constants, at t = 0 . If the resistance of the loop is R then the heat generated in the loop after a long time $(t-\infty )$ is: [JEE ONLINE 10-04-2016]

A)
$\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}R}{\tau }$

B)
$\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{2\tau R}$

C)
$\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{\tau R}$

D)
$\frac{{{\pi }^{2}}{{r}^{4}}B_{0}^{2}}{2\tau R}$

• question_answer46)  Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed 'v' in a uniform magnetic field B going into the plane of the paper (see figure) . If charge densities ${{\sigma }^{1}}$and ${{\sigma }^{2}}$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) [JEE ONLINE 10-04-2016]

A)
${{\sigma }_{1}}=\frac{-{{\varepsilon }_{0}}vB}{2},\,{{\sigma }_{2}}=\frac{-2{{\varepsilon }_{0}}vB}{2}$

B)
${{\sigma }_{1}}={{\sigma }_{2}}={{\varepsilon }_{0}}vB$

C)
${{\sigma }_{1}}=\frac{{{\varepsilon }_{0}}vB}{2},\,{{\sigma }_{2}}=\frac{-{{\varepsilon }_{0}}vB}{2}$

D)
${{\sigma }_{1}}={{\varepsilon }_{0}}vB,\,{{\sigma }_{2}}=-{{\varepsilon }_{0}}vB$

• question_answer47)  In a coil of resistance $100\,\Omega ,$ a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:                                [JEE Main 2017]

A)
250 Wb

B)
275 Wb

C)
200 Wb

D)
225 Wb

• question_answer48) A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current $I={{I}_{0}}\cos (\omega t).$The emf induced in the smaller inner loop is nearly? [JEE Online 08-04-2017]

A)
$\pi {{\mu }_{0}}{{I}_{0}}\frac{{{a}^{2}}}{b}\omega \sin (\omega t)$

B)
$\frac{\pi {{\mu }_{0}}{{I}_{0}}}{2}.\frac{{{a}^{2}}}{b}\omega \cos (\omega t)$

C)
$\frac{\pi {{\mu }_{0}}{{I}_{0}}{{b}^{2}}}{a}\omega \cos (\omega t)$

D)
$\frac{\pi {{\mu }_{0}}{{I}_{0}}}{2}.\frac{{{a}^{2}}}{b}\omega \sin (\omega t)$

• question_answer49) An ideal capacitor of capacitance $0.2\mu F$ is charged to a potential difference of $10V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self-inductance$0.5mH$. The current at a time when the potential difference across the capacitor is $5V$, is:                                    [JEE Online 15-04-2018]

A)
0.17 A

B)
0.15 A

C)
0.34 A

D)
0.25 A

• question_answer50) At the centre of a fixed large circular coil of radius $R$, a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $I$. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation.            [JEE Online 15-04-2018 (II)]

A)
$\frac{{{\mu }_{0}}I}{2R}\omega {{r}^{2}}\sin \omega t$

B)
$\frac{{{\mu }_{0}}I}{4R}\omega \pi {{r}^{2}}\sin \omega t$

C)
$\frac{{{\mu }_{0}}I}{2R}\omega \pi {{r}^{2}}\sin \omega t$

D)
$\frac{{{\mu }_{0}}I}{4R}\omega {{r}^{2}}\sin \omega t$

• question_answer51) A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity$\omega ,$the maximum e.m.f. induced in the coil will be [JEE Main Online 16-4-2018]

A)
$nBA\omega$

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

C)
$3nBA\omega$

D)
$\frac{1}{2}nBA\omega$

• question_answer52) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5A, and its efficiency is 90%, the output current would be:[JEE Main Online 16-4-2018]

A)
20 A

B)
45 A

C)
45 A

D)
25 A

• question_answer53) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is $90%$, the output current would be:  [JEE Main 09-Jan-2019 Evening]

A)
45 A

B)
35 A

C)
25 A

D)
50 A

• question_answer54) A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron $=1.6\,\times \,{{10}^{-19}}C$) [JEE Main 09-Jan-2019 Evening]

A)
$1.6\times {{10}^{-19}}kg$

B)
$1.6\times {{10}^{-27}}\text{ }kg$

C)
$9.1\times {{10}^{-}}^{31}kg$

D)
$2.0\times {{10}^{-}}^{24}kg$

• question_answer55) The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is-                                     [JEE Main 10-Jan-2019 Evening]

A)
740 J

B)
637.5 J

C)
540 J

D)
437.5 J

• question_answer56) A particle of mass m and charge q is in an electric and magnetic field given by $\vec{E}=2\hat{i}+3\hat{j};\vec{B}=4\hat{j}+6\hat{k}.$ The charged particle is shifted from the origin to the point $P(x=1;y=1)$along a straight path. The magnitude of the total work done is-                                                                [JEE Main 11-Jan-2019 Evening]

A)
(0.15)q

B)
(0.35)q

C)
(2.5)q

D)
5q

• question_answer57) The region between$y=0$and$y=d$contains a magnetic field $\vec{B}=B\overset{\wedge }{\mathop{z}}\,.$ A particle of mass m and charge q enters the region with a velocity $\vec{v}=v\hat{i}.$ If $d=\frac{mv}{2qB},$ the acceleration of the charged particle at the point of its emergence at the other side is           [JEE Main 11-Jan-2019 Evening]

A)
$\frac{qvB}{m}\left( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)$

B)
$\frac{qvB}{m}\left( \frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j} \right)$

C)
$\frac{qvB}{m}\left( \frac{1}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j} \right)$

D)
None of these

• question_answer58)  A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is:      [JEE Main 8-4-2019 Morning]

A)
$\frac{2}{\ell n2}$

B)
$\ell n2$

C)
$2\ell n2$

D)
$\frac{1}{2}\ell n2$

• question_answer59)  A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 $N{{m}^{-1}}$ (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillation it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance $10\Omega$and air drag negligible, N will be close to : [JEE Main 8-4-2019 Morning]

A)
50000

B)
5000

C)
10000

D)
1000

• question_answer60) The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:            [JEE Main 9-4-2019 Morning]

A)
$1/{{L}^{2}}$

B)
$1/L$

C)
$L$

D)
${{L}^{2}}$

• question_answer61) Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of ${{10}^{-3}}$Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-    [JEE Main 9-4-2019 Afternoon]

A)
$6.67\times {{10}^{3}}Wb$

B)
$6.67\times {{10}^{4}}Wb$

C)
$3.67\times {{10}^{4}}Wb$

D)
$3.67\times {{10}^{3}}Wb$

• question_answer62) A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10A, then the input voltage and current in the primary coil are: [JEE Main 10-4-2019 Morning]

A)
220 V and 10A

B)
440 V and 5A

C)
440 V and 20 A

D)
220 V and 20 A

• question_answer63) A coil of self inductance 10 mH and resistance $0.1\Omega$ is connected through a switch to a battery of internal resistance $0.9\Omega .$After the switch is closed, the time taken for the current to attain 80% of the saturation value is : (Take $\ln 5=1.6$) [JEE Main 10-4-2019 Afternoon]

A)
0.103 s

B)
0.016 s

C)
0.002 s

D)
0.324 s

• question_answer64)  The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of $1cm{{s}^{-1}}.$ At some instant, a part of L is in a uniform magnetic field of 1T, perpendicular to the plane of the loop. If the resistance of L is $1.7\Omega ,$the current in the loop at that instant will be close to: [JEE Main Held on 12-4-2019 Morning]

A)
$115\mu A$

B)
$170\mu A$

C)
$60\mu A$

D)
$150\mu A$

• question_answer65)  An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $\vec{B}=(1.5\times {{10}^{-3}}T)\hat{k}$at S (See figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is : (electron's charge $=1.6\times {{10}^{19}}C,$ mass of electron $=9.1\times {{10}^{31}}\text{ }kg$) [JEE Main 12-4-2019 Afternoon]

A)
12.87 cm

B)
1.22 cm

C)
11.65 cm

D)
2.25 cm

• question_answer66) A long solenoid of radius R carries a time (t) - dependent current $I(t)={{I}_{0}}t(1-t)$. A ring of radius 2R is placed coaxially near its middle. During the time interval $0\le t\le 1$, the induced current $({{I}_{R}})$ and the induced $EMF({{V}_{R}})$ in the ring change as: [JEE MAIN Held on 07-01-2020 Morning]

A)
Direction of ${{I}_{R}}$ remains unchanged and ${{V}_{R}}$is zero at t = 0.25

B)
Direction of ${{I}_{R}}$ remains unchanged and ${{V}_{R}}$ is maximum at t = 0.5

C)
At t = 0.5 direction of ${{I}_{R}}$ reverses and ${{V}_{R}}$is zero

D)
At t = 0.25 direction of ${{I}_{R}}$ reverses and ${{V}_{R}}$ is maximum

• question_answer67) Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ${{\phi }_{i}}$ . The magnetic flux through the area of the circular coil area is given by ${{\phi }_{0}}$ . Which of the following option is correct? [JEE MAIN Held on 07-01-2020 Morning]

A)
${{\phi }_{i}}=-{{\phi }_{0}}$

B)
${{\phi }_{i}}<{{\phi }_{0}}$

C)
${{\phi }_{i}}={{\phi }_{0}}$

D)
${{\phi }_{i}}>{{\phi }_{0}}$

• question_answer68) A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0,5, 5) and F(0, 0, 5). The magnetic field in this region is $\overrightarrow{B}=\left( 3\hat{i}+4\hat{k} \right)T$. The quantity of flux through the loop ABCDEFA (in Wb) is ________. [JEE MAIN Held on 07-01-2020 Morning]

• question_answer69) An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and $5\,\Omega$resistor. The ratio of the currents a time $t=\,\,\infty$ and at $t=40$s is close to (Take${{e}^{2}}=7.389$) [JEE MAIN Held on 07-01-2020 Evening]

A)
1.06

B)
1.15

C)
1.46

D)
0.84