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Class 12 • Physics
Electromagnetic Induction
Chapter-6
363 Questions
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41 Easy313 Medium9 Hard
Practice Questions
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1
MediumAiims2019
Assertion : A metallic surface is moved in and out in magnetic field then emf is induced in it. Reason : Eddy current will be produced in a metallic surface moving in and out of magnetic field.
Options:
A) If both assertion and reason are true and reason
is the correct explanation of assertion.
B) If both assertion and reason are true, but reason
is not the correct explanation of assertion.
C) If assertion is true, but reason is false.
D) If both assertion and reason are false.
2
MediumAiims2018
A system $S consists of two coils A and B. The coil A carries a steady current I. While the coil B$ is suspended nearby as shown in figure. Now, if the system is heated, so as to raise the temperature of two coils steadily, then
Options:
A) the two coils shows attraction
B) the two coils shows repulsion
C) there is no change in the position of the two coils
D) induced current are not possible in coil $B
3
MediumAiims2018
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 on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 20 A flows through the smaller loop, then the flux linked with bigger drop is
Options:
A) 9.1 \times 10^{-11} \mathrm{~Wb}
B) 6 \times 10^{-11} \mathrm{~Wb}
C) 3.3 \times 10^{-11} \mathrm{~Wb}
D) 6.6 \times 10^{-9} \mathrm{~Wb}
4
MediumBITSAT2024
Inside a solenoid of radius 0.5 m , magnetic field is changing at a rate of 50 \times 10^{-6} \mathrm{~T} / \mathrm{s} . Acceleration of an electron placed at a distance of 0.3 m from axis of solenoid will be
Options:
A) 23 \times 10^{6} \mathrm{~ms}^{-2}
B) 26 \times 10^{6} \mathrm{~m} / \mathrm{s}^{2}
C) 1.3 \times 10^{9} \mathrm{~ms}^{-2}
D) 26 \times 10^{9} \mathrm{~m} / \mathrm{s}^{2}
5
MediumBITSAT2021
Two coils A and B have a mutual inductance 0.001 H. The current changes in the first coil according to the equation $i = {i_0}\sin \omega t, where i0 = 10A and \omega = 10\pi rads-$1. The maximum value of emf in the second coil is
Options:
A) 0.01 $\pi$ V
B) 1 $\pi$ V
C) 0.1 $\pi$ V
D) 0.05 $\pi$ V
6
MediumBITSAT2020
Given that in a fluorescent lamp's choke, a reverse voltage of 120 V is generated as the choke's current changes steadily from 0.50 A to 0.20 A in a time frame of 0.030 ms. Calculate the self inductance of the choke in millihenrys (mH).
Options:
A) 12 H
B) 12 $\times 10-$3 mH
C) 12 $\times 10-$3 H
D) 0
7
MediumCOMEDK2025
A rectangular coil of 250 turns has an average area of 20 \mathrm{~cm} \times 15 \mathrm{~cm}. The coil rotates with a speed of 60 cycles per second in a uniform magnetic field of 2 \times 10^{-2} \mathrm{~T} about an axis perpendicular to the field. The peak value of the induced emf is:
Options:
A) 36 \pi volt
B) 30 \pi volt
C) 18 \pi volt
D) 12 \pi volt
8
MediumCOMEDK2025
A circular coil of area 2 \sqrt{2} \mathrm{~cm}^2 and resistance 2 \boldsymbol{\Omega} is arranged vertically in the east -west direction. A uniform magnetic field 0.2 T is set up across the plane in the north to east direction. Now the magnetic field is removed at a steady rate in 0.4 s What is the current developed in the coil?
Options:
A) 0.5 \times 10^{-3} A
B) 0.5 \times 10^{-4} A
C) 1 \times 10^{-4} A
D) 0.5 \times 10^{-5} A
9
MediumCOMEDK2025
A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is 2000 \times 10^{-6} weber. What is the induced emf in the secondary if the current through the primary increases at a rate of 0.2 \mathrm{As}^{-1} ?
Options:
A) 2 \times 10^{-4} V
B) 4 \times 10^{-4} V
C) 1 \times 10^{-4} V
D) 8 \times 10^{-4} V
10
MediumCOMEDK2025
The magnetic flux \phi through a stationary loop of wire having a resistance R varies with time as \phi=4 t^2+3 t. The average emf and total charge flowing in the loop in the time interval t=0 to t=\tau respectively are
Options:
A) \tau+3, \quad \frac{4 \tau^2+3 \tau}{R}
B) 3 \tau+4, \quad \frac{4 \tau^2+3 \tau}{R}
C) 4 \tau+3, \quad \frac{4 r+3}{R}
D) 4 \tau+3, \quad \frac{4 \tau^2+3 \tau}{R}
11
MediumCOMEDK2024
A conducting circular loop is placed in a uniform magnetic field $\mathrm{B}=0.125 \mathrm{~T} with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of 2 \mathrm{~mm} \mathrm{~s}^{-1}, then the induced emf when the radius is 4 \mathrm{~cm}$ is
Options:
A) 0.52 \pi \mu V
B) 20 \pi \mu V
C) \frac{2}{3}\mu V
D) \frac{3 \pi}{2} \mu V
12
MediumCOMEDK2024
A transformer of $100 \% efficiency has 200 turns in the primary and 40000 turns in the secondary. It is connected to a 220 \mathrm{~V} main supply and secondary feeds to a 100 \mathrm{~K} \Omega$ resistance. The potential difference per turn is
Options:
A) 11 V
B) 18 V
C) 25 V
D) 1.1 V
13
MediumCOMEDK2024
The current in a coil changes steadily from $3 \mathrm{~A} to 5 \mathrm{~A} in 0.2 \mathrm{~s} when an emf of 2 \mu \mathrm{V}$ is induced in it. The self-inductance of the coil is
Options:
A) 0.2 mH
B) 20 $\mu H
C) 2 $\mu H
D) 0.2 $\mu H
14
MediumCOMEDK2024
The magnetic flux linked with a coil is given by the equation: $\phi=8 t^2+t+10. The e.m.f. induced in the coil in the 3^{\text {rd }}$ second will be
Options:
A) 49 V
B) 33 V
C) 16 V
D) 20 V
15
MediumCOMEDK2024
A wire ' 1 ' $\mathrm{cm} long bent into a circular loop is placed perpendicular to the magnetic field of flux density 'B^{\prime} W b \mathrm{~m}^{-2}. Within 0.1 \mathrm{sec}, the loop is changed into a square of side 'a' \mathrm{cm}$ and flux density is doubled. The value of e.m.f. induced is
Options:
A)
\frac{-5 B\left(8 л \mathrm{a}^2-\mathrm{l}^2\right)}{2}
B)
\frac{5 B\left(8 л a^2-l^2\right)}{2 л}
C)
\frac{-5 B\left(8 л a^2-l^2\right)}{2 л}
D)
\frac{-5 B\left(8 a^2-l^2\right)}{2 \pi}
16
MediumCOMEDK2024
In an inductor of self-inductance $2 \mathrm{~mH}, current changes with time (in sec) according to the relation, I=(3 t^2-3 t+8) A$. The emf becomes zero at
Options:
A) 2 sec
B) 6 sec
C) 0.5 sec
D) 5 sec
17
MediumCOMEDK2024
A metallic rod of length '$a' is rotated with an angular frequency of 0.2 \mathrm{~rads}^{-1} about an axis normal to the rod passing through its one end. A constant and uniform magnetic field of '\mathrm{B}$' T parallel to the axis exists everywhere. The emf developed across the ends of the rod is
Options:
A) \frac{\mathrm{Ba}^2}{10}
B) \frac{\mathrm{Ba}^2}{5}
C) \frac{\mathrm{Ba}^2}{50}
D) \frac{\mathrm{Ba}^2}{2}
18
MediumCOMEDK2024
Select the unit of the coefficient of mutual induction from the following.
Options:
A) volt. second / ampere
B) weber. ampere
C) ampere / weber
D) volt. ampere / second
19
MediumCOMEDK2024
Around the central part of an air cored solenoid of length $20 \mathrm{~cm} and area of cross section 1.4 \times 10^{-3} \mathrm{~m}^2 and 3000 turns, another coil of 250 turns is closely wound. A current 2 \mathrm{~A} in the solenoid is reversed in 0.2 \mathrm{~s}$, then the induced emf produced is
Options:
A) 1.32 \times 10^{-1} \mathrm{~V}
B) 4 \times 10^{-1} \mathrm{~V}
C) 1.16 \times 10^{-1} \mathrm{~V}
D) 8 \times 10^{-2} \mathrm{~V}
20
MediumCOMEDK2024
A metallic rod of $2 \mathrm{~m} length is rotated with a frequency 100 \mathrm{~Hz} about an axis passing through the centre of the circular ring of radius 2 \mathrm{~m}. A constant magnetic field 2 \mathrm{~T}$ is applied parallel to the axis and perpendicular to the length of the rod. The emf developed across the ends of the rod is :
Options:
A) 800 $\pi$ volt
B) 1600 $\pi$ volt
C) 1600 volt
D) 400 $\pi$ volt
21
MediumCOMEDK2023
The magnetic flux linked with a coil satisfies the relation $\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}, where t is time in second. The emf induced in the coil at t=2 \mathrm{~s}$ is
Options:
A) 22 V
B) 18 V
C) 16 V
D) 40 V
22
MediumCOMEDK2023
One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from $3 \mathrm{~A} to 1 \mathrm{~A}$ in 100 milliseconds. the mutual inductance of the two coil is:
Options:
A) 0.5 H
B) 0.25 H
C) 0.005 H
D) 0.05 H
23
MediumCOMEDK2022
Television frequencies are of the order of 100 MHz, while radio frequencies are of the order of 1 MHz. Using these as typical frequencies, the ratio of the emf generated in a loop antenna by a television wave to that generated by a radio wave, if both have equal electric field intensities.
Options:
A) 1
B) 10
C) 100
D) 66.6
24
MediumCOMEDK2022
A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5 A, then the average force on each electron in the coil due to the magnetic field is
Options:
A) 2.5\times10^{-25}$ N
B) 4.5\times10^{-25}$ N
C) 5\times10^{-25}$ N
D) 5.5\times10^{-25}$ N
25
MediumCOMEDK2020
A coil of wire of a certain radius has 100 turns and a self inductance of 15 mH. The self inductance of a second similar coil of 500 turns will be
Options:
A) 75 mH
B) 375 mH
C) 15 mH
D) None of the above
26
MediumCOMEDK2020
A coil of 100 turns carries a current of 5 mA and creates a magnetic flux of 10$^{-5}$ Wb. The inductance is
Options:
A) 0.2 mH
B) 2.0 mH
C) 0.02 mH
D) None of these
27
MediumCOMEDK2020
In step-up transformer, relation between number of turns in primary (N$_P) and number of turns in secondary (N_S$) coils is
Options:
A) N$_S is greater than N_P
B) N$_P is greater than N_S
C) N$_S is equal to N_P
D) N$_P = 2N_S
28
HardJee Advance2025
A conducting square loop initially lies in the X Z plane with its lower edge hinged along the X-axis. Only in the region y \geq 0, there is a time dependent magnetic field pointing along the Z-direction, \vec{B}(t)=B_0(\cos \omega t) \hat{k}, where B_0 is a constant. The magnetic field is zero everywhere else. At time t=0, the loop starts rotating with constant angular speed \omega about the X axis in the clockwise direction as viewed from the +X axis (as shown in the figure). Ignoring self-inductance of the loop and gravity, which of the following plots correctly represents the induced e.m.f. (V) in the loop as a function of time:
Options:
A)
B)
C)
D)
29
HardJee Advance2024
A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field \vec{B} pointing in the +z-direction. A conducting loop \mathrm{PQR}, in the form of an equilateral triangle of the same height L, is placed in the x-y plane with its vertex \mathrm{P} at x=0 in the orientation shown in the figure. At t=0, the loop starts entering the region of the magnetic field with a uniform velocity \vec{v} along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion. Which of the following graph best depicts the variation of the induced emf (E) in the loop as a function of the distance (x) starting from x=0 ?
Options:
A)
B)
C)
D)
30
HardJee Advance2023
A thin conducting rod M N of mass 20 ~\mathrm{gm}, length 25 \mathrm{~cm} and resistance 10 ~\Omega is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field B_0=4 \mathrm{~T} directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time t=0 and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-I with an appropriate value from List-II, and choose the correct option. [Given: The acceleration due to gravity g=10 \mathrm{~m} \mathrm{~s}^{-2} and e^{-1}=0.4 ] List - I List - II (P) At t=0.2 \mathrm{~s}, the magnitude of the induced emf in Volt (1) 0.07 (Q) At t=0.2 \mathrm{~s}, the magnitude of the magnetic force in Newton (2) 0.14 (R) At t=0.2 \mathrm{~s}, the power dissipated as heat in Watt (3) 1.20 (S) The magnitude of terminal velocity of the rod in \mathrm{m} \mathrm{s}^{-1} (4) 0.12 (5) 2.00
Options:
A) P \rightarrow 5, Q \rightarrow 2, R \rightarrow 3, S \rightarrow 1
B) P \rightarrow 3, Q \rightarrow 1, R \rightarrow 4, S \rightarrow 5
C) P \rightarrow 4, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 2
D) P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 5
31
HardJee Advance2009
The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1 and I_2$ are the currents in the segments ab and cd. Then,
Options:
A) I_1 > I_2
B) I_1 < I_2
C) I_1 is in the direction ba and I_2$ is in the direction cd.
D) I_1 is in the direction ab and I_2$ is in the direction dc.
32
MediumJee Advance2006
Modern trains are based on Maglev technology in which trains are magnetically levitated, which runs its EDS Maglev system. There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If train lowers down, then according to Lenz's law, a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force due to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing the power consumption and enabling the train to attain very high speeds. Disadvantages of Maglev train is that as it slows down, t the electromagnetic forces decreases and it becomes difficult to keep levitated and as it moves forward according to Lenz law there is electromagnetic drag force.
Options:
A) No friction hence no power consumption.
B) No electric power is used.
C) Gravitation force is zero.
D) Electrostatic force draws the train.
33
MediumJee Advance2006
Modern trains are based on Maglev technology in which trains are magnetically levitated, which runs its EDS Maglev system. There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If train lowers down, then according to Lenz's law, a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force due to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing the power consumption and enabling the train to attain very high speeds. Disadvantages of Maglev train is that as it slows down, t the electromagnetic forces decreases and it becomes difficult to keep levitated and as it moves forward according to Lenz law there is electromagnetic drag force.
Options:
A) Train experiences upward force according to Lenz's law
B) Friction force creates a drag on the train.
C) Retardation.
D) By Lenz's law, train experiences a drag.
34
MediumJee Advance2006
Modern trains are based on Maglev technology in which trains are magnetically levitated, which runs its EDS Maglev system. There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If train lowers down, then according to Lenz's law, a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force due to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing the power consumption and enabling the train to attain very high speeds. Disadvantages of Maglev train is that as it slows down, t the electromagnetic forces decreases and it becomes difficult to keep levitated and as it moves forward according to Lenz law there is electromagnetic drag force.
Options:
A) Electrostatic force.
B) Time-varying electric field.
C) Magnetic force.
D) Induced electric field
35
MediumJee Advance2005
A long solenoid of radius a and number of turns per unit length $n is enclosed by cylindrical shell of radius R, thickness d (d < < R) and length L. A variable current \mathrm{I}=\mathrm{I}_{0} \sin \omega t flows through the coil. If the resistivity of the material of cylindrical shell is \mathrm{P}$, find the induced current in the shell.
Options:
A) \mathrm{I}=\frac{\left(\mu_{0} \mathrm{~L} d n a^{2} \mathrm{I}_{0} \omega \cos \omega t\right)}{\rho \mathrm{R}}
B) \mathrm{I}=\frac{\left(3\mu_{0} \mathrm{~L} d n a^{2} \mathrm{I}_{0} \omega \cos \omega t\right)}{2 \rho \mathrm{R}}
C) \mathrm{I}=\frac{\left(\mu_{0} \mathrm{~L} d n a^{2} \mathrm{I}_{0} \omega \cos \omega t\right)}{2 \rho \mathrm{R}}
D) \mathrm{I}=\frac{3\left(\mu_{0} \mathrm{~L} d n a^{2} \mathrm{I}_{0} \omega \cos \omega t\right)}{ \rho \mathrm{R}}
36
MediumJee Advance2025
A conducting square loop of side L, mass M and resistance R is moving in the X Y plane with its edges parallel to the X and Y axes. The region y \geq 0 has a uniform magnetic field, \vec{B}=B_0 \widehat{k}. The magnetic field is zero everywhere else. At time t=0, the loop starts to enter the magnetic field with an initial velocity v_0 \hat{\jmath} \mathrm{~m} / \mathrm{s}, as shown in the figure. Considering the quantity K=\frac{B_0^2 L^2}{R M} in appropriate units, ignoring self-inductance of the loop and gravity, which of the following statements is/are correct:
Options:
A) If v_0 = 1.5KL, the loop will stop before it enters completely inside the region of magnetic field.
B) When the complete loop is inside the region of magnetic field, the net force acting on the loop is zero.
C) If v_0 = \frac{KL}{10}, the loop comes to rest at t = \left(\frac{1}{K}\right) \ln\left(\frac{5}{2}\right).
D) If v_0 = 3KL, the complete loop enters inside the region of magnetic field at time t = \left(\frac{1}{K}\right) \ln\left(\frac{3}{2}\right).
37
HardJee Advance2019
A conducting wire of parabolic shape, initially y = x2, is moving with velocity $v = {v_0}\widehat i in a non-uniform magnetic field B = {B_0}\left( {1 + {{\left( {{y \over L}} \right)}^\beta }} \right)\widehat k, as shown in figure. If V0, B0, L and \beta are positive constants and \Delta \phi $ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are
Options:
A) \left| {\Delta \phi } \right| = {4 \over 3}{B_0}{V_0}L for \beta $ = 2
B) \left| {\Delta \phi } \right| remains the same if the parabolic wire is replaced by a straight wire, y =x initially, of length \sqrt 2 L
C) \left| {\Delta \phi } \right| = {1 \over 2}{B_0}{V_0}L for \beta $ = 0
D) \left| {\Delta \phi } \right|$ is proportional to the length of the wire projected on the y-axis.
38
MediumJee Advance2018
In the figure below, the switches ${S_1} and {S_2} are closed simultaneously at t=0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wire reaches its maximum magnitude {I_{\max }} at time t = \tau $ . Which of the following statements is (are) true?
Options:
A) {I_{\max }} = {V \over {2R}}
B) {I_{max}} = {V \over {4R}}
C) \tau = {L \over R}\ln 2
D) \tau = {{2L} \over R}\ln 2
39
MediumJee Advance2017
A source of constant voltage V is connected to a resistance R and two ideal inductors L1 and L2 through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?
Options:
A) After a long time, the current through L1 will be ${V \over R}{{{L_2}} \over {{L_1} + {L_2}}}
B) After a long time, the current through L2 will be ${V \over R}{{{L_1}} \over {{L_1} + {L_2}}}
C) The ratio of the currents through L1 and L2 is fixed at all times (t > 0)
D) At t = 0, the current through the resistance R is ${V \over R}
40
HardJee Advance2017
A circular insulated copper wire loop is twisted to form two loops of area $A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field \overrightarrow B points into the plane of the paper. At t=0, the loop starts rotating about the common diameter as axis with a constant angular velocity \omega $ in the magnetic field. Which of the following options is/are correct?
Options:
A) The emf induced in the loop is proportional to the sum of the areas of the two loops
B) The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude if maximum emf induced in the smaller loop alone
C) The net emf induced due to both the loops is proportional to $\cos \,\omega t
D) The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper
41
HardJee Advance2016
A rigid wire loop of square shape having side of length L and resistance R is moving along the X-axis with a constant velocity v0 in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field B0 into the plane of the paper, as shown in the figure. For sufficiently large v0, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x. Counter-clockwise current is taken as positive. Which of the following schematic plot(s) is (are) correct? (Ignore gravity)
Options:
A)
B)
C)
D)
42
HardJee Advance2016
A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90$^\circ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 As-$1. Which of the following statement(s) is (are) true?
Options:
A) There is a repulsive force between the wire and the loop.
B) If the loop is rotated at a constant angular speed about the wire, an additional emf of $\left( {{{{\mu _0}} \over \pi }} \right)$ volt is induced in the wire
C) The magnitude of induced emf in the wire is $\left( {{{{\mu _0}} \over \pi }} \right)$ volt
D) The induced current in the wire is in opposite direction to the current along the hypotenuse.
43
MediumJee Advance2012
A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it, the correct statement(s) is(are)
Options:
A) the emf induced in the loop is zero if the current is constant.
B) the emf induced in the loop is finite if the current is constant.
C) the emf induced in the loop is zero if the current decreases at a steady state
D) the emf induced in the loop is finite if the current decreases at a steady state.
44
MediumJee Advance2009
Two metallic rings A and B, identical in shape and size but having different resistivities $\rho_A and \rho_B, are kept on top of two identical solenoids as shown in the figure below. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights h_A and h_B, respectively, with h_A > h_B. The possible relation(s) between their resistivities and their masses m_A and m_B$ is (are)
Options:
A) \rho_A > \rho_B and m_A = m_B
B) \rho_A < \rho_B and m_A = m_B
C) \rho_A > \rho_B and m_A > m_B
D) \rho_A < \rho_B and m_A < m_B
45
MediumJee Advance2022
Consider an LC circuit, with inductance L=0.1 \,\mathrm{H} and capacitance C=10^{-3} \mathrm{~F}, kept on a plane. The area of the circuit is 1 \mathrm{~m}^{2}. It is placed in a constant magnetic field of strength B_{0} which is perpendicular to the plane of the circuit. At time t=0, the magnetic field strength starts increasing linearly as B=B_{0}+\beta t with \beta=0.04 \,\mathrm{T\,s}^{-1}. The maximum magnitude of the current in the circuit is _________ m A.
Options:
46
MediumJee Advance2020
The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistors, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced EMF in the inductors by the time the currents reach their steady state values is _________ mJ.
Options:
47
EasyJee Advance2019
A 10 cm long perfectly conducting wire PQ is moving with a velocity I cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1$\Omega as shown in figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is x \times $ 10-3 A, where the value of x is ........... [Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given e-1 = 0.37, where e is base of the natural logarithm]
Options:
48
MediumJee Advance2016
Two inductors L1 (inductance 1mH, internal resistance 3$\Omega) and L2 (inductance 2 mH, internal resistance 4\Omega), and a resistor R (resistance 12\Omega$) are all connected in parallel across a 5V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (Imax / Imin) drawn from the battery is
Options:
49
MediumJee Advance2012
A circular wire loop of radius R is placed in the xy plane centred at the origin O. A square loop of side a(a << R) having two turns is placed with its centre at z = $\sqrt3R along the axis of the circular wire loop, as shown in the figure. The plane of the square loop makes an angle of 45^\circ with respect to z-axis. If the mutual inductance between the loops is given by {{{\mu _0}{a^2}} \over {{2^{p/2}}R}}$, then the value of p is ___________.
Options:
50
EasyJEE Mains2026
\text { Match the LIST-I with LIST-II } $ List-I List-II A. Magnetic induction I. <mi mathvariant="normal">M</mi> <mi mathvariant="normal">L</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">L</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> MLT^(-2)A^(-2) B. Magnetic flux II. <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> ML^(2)T^(-2)A^(-2) C. Magnetic permeability III. <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>0</mn> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>0</mn> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> ML^(0)T^(-2)A^(-1) D. Self inductance IV. <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext> </mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mi mathvariant="normal">M</mi> <mrow data-mjx-texclass="ORD"> <mi mathvariant="normal">L</mi> </mrow> <mn>2</mn> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">T</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>2</mn> </mrow> <mrow data-mjx-texclass="ORD"> <mtext></mtext> <mi mathvariant="normal">A</mi> </mrow> <mrow data-mjx-texclass="ORD"> <mo>−</mo> <mn>1</mn> </mrow> ML^(2)T^(-2)A^(-1) Choose the correct answer from the options given below:
Options:
A) A-III, B-IV, C-II, D-I
B) A-I, B-III, C-IV, D-II
C) A-IV, B-III, C-I, D-II
D) A-III, B-IV, C-I, D-II
51
EasyJEE Mains2026
A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is \_\_\_\_ mV.
Options:
A) 13.2
B) 6.6
C) 1.32
D) 8.25
52
MediumJEE Mains2026
Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I=10 \sin (\omega \mathrm{t}) \mathrm{A}, where \omega=1000 \mathrm{rad} . / \mathrm{s}. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed v=1 \mathrm{~cm} / \mathrm{s}. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is ${\alpha \over {\sqrt 2 }}\mu A. The value of \alpha is \_\_\_\_ . [Resistance of the loop =10 \Omega$ ]
Options:
A) 80
B) 280
C) 100
D) 197
53
EasyJEE Mains2026
A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity \left(g=10 \mathrm{~m} / \mathrm{s}^2\right) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of 200 m is \_\_\_\_ mV .
Options:
A) 200 \sqrt{10}
B) 0.2 \sqrt{10}
C) 20 \sqrt{10}
D) 2 \sqrt{10}
54
MediumJEE Mains2026
Figure shows the circuit that contains three resistances ( 9 \Omega each) and two inductors ( 4 mH each). The reading of ammeter at the moment switch K is turned ON , is \_\_\_\_ A.
Options:
A) 2
B) 3
C) 1
D) zero
55
MediumJEE Mains2026
X P Q Y is a vertical smooth long loop having a total resistance R where P X is parallel to Q Y and separation between them is l. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod C D of length L(L>l) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is \_\_\_\_ \mathrm{m} / \mathrm{s} .(\mathrm{g}= acceleration due to gravity)
Options:
A) \frac{m \mathrm{~g} R}{B^2 l^2}
B) \frac{2 m g R}{B^2 L^2}
C) \frac{2 m g R}{B^2 l^2}
D) \frac{8 m g R}{B^2 l^2}
56
MediumJEE Mains2026
Three identical coils C_1, C_2 and C_3 are closely placed such that they share a common axis. C_2 is exactly midway. C_1 carries current I in anti-clockwise direction while C_3 carries current I in clockwise direction. An induced current flows through C_2 will be in clockwise direction when
Options:
A) C_1 and C_3 move with equal speeds away from C_2
B) C_1 moves towards C_2 and C_3 moves away from C_2
C) C_1 and C_3 move with equal speeds towards C_2
D) C_1 moves away from C_2 and C_3 moves towards C_2
57
MediumJEE Mains2026
A conducting circular loop of area 1.0 \mathrm{~m}^2 is placed perpendicular to a magnetic field which varies as B=\sin (100 t) Tesla. If the resistance of the loop is 100 \Omega, then the average thermal energy dissipated in the loop in one period is \_\_\_\_ J.
Options:
A) \pi^2
B) \frac{\pi}{2}
C) \pi
D) 2 \pi
58
EasyJEE Mains2026
A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T . If the resistance of the total circuit is 2 \Omega then the force needed to move the rod towards right with constant speed (v) of 1.5 \mathrm{~m} / \mathrm{s} is \_\_\_\_ N.
Options:
A) 5.7 \times 10^{-2}
B) 7.5 \times 10^{-3}
C) 5.7 \times 10^{-3}
D) 7.5 \times 10^{-2}
59
MediumJEE Mains2025
A coil of area A and N turns is rotating with angular velocity \omega in a uniform magnetic field \vec{B} about an axis perpendicular to \vec{B}. Magnetic flux \varphi and induced emf \varepsilon across it, at an instant when \vec{B} is parallel to the plane of coil, are :
Options:
A) φ = AB, φ = NABω
B) φ = AB, φ = 0
C) φ = 0, ε = 0
D) φ = 0, ε = NABω
60
EasyJEE Mains2025
Consider I1 and I2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L1 = self inductance of coil 1, M12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be :
Options:
A) e1 = -L1\frac{dI_2}{dt} - M12\frac{dI_1}{dt}
B) e1 = -L1\frac{dI_1}{dt} + M12\frac{dI_2}{dt}
C) e1 = -L1\frac{dI_1}{dt} - M12\frac{dI_1}{dt}
D) e1 = -L1\frac{dI_1}{dt} - M12\frac{dI_2}{dt}
61
EasyJEE Mains2025
A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10 \pi rad s-1 about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? (\pi=3.14)
Options:
A) 0.5024 V
B) 0.0628 V
C) 0.2512 V
D) 0.1256 V
62
MediumJEE Mains2025
Regarding self-inductance: A. The self-inductance of the coil depends on its geometry. B. Self-inductance does not depend on the permeability of the medium. C. Self-induced e.m.f. opposes any change in the current in a circuit. D. Self-inductance is electromagnetic analogue of mass in mechanics. E. Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:
Options:
A) A, B, C, E only
B) A, B, C, D only
C) A, C, D, E only
D) B, C, D, E only
63
EasyJEE Mains2025
A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf (\varepsilon) with time (t) is given by
Options:
A)
B)
C)
D)
64
EasyJEE Mains2024
A square loop of side $15 \mathrm{~cm} being moved towards right at a constant speed of 2\mathrm{~cm} / \mathrm{s} as shown in figure. The front edge enters the 50 \mathrm{~cm} wide magnetic field at t=0. The value of induced emf in the loop at t=10 \mathrm{~s}$ will be :
Options:
A) zero
B) 4.5 mV
C) 0.3 mV
D) 3 mV
65
EasyJEE Mains2024
In a coil, the current changes from $-2 \mathrm{~A} to +2 \mathrm{~A} in 0.2 \mathrm{~s} and induces an emf of 0.1 \mathrm{~V}$. The self inductance of the coil is :
Options:
A) 4 mH
B) 2.5 mH
C) 1 mH
D) 5 mH
66
MediumJEE Mains2024
Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:
Options:
A) \frac{\mu_o}{2 \pi} \cdot \frac{b^2}{a}
B) \frac{\mu_{\mathrm{o}} \pi \mathrm{a}^2}{2 \mathrm{~b}}
C) \frac{\mu_0 \pi b^2}{2 a}
D) \frac{\mu_0}{2 \pi} \cdot \frac{a^2}{b}
67
EasyJEE Mains2024
A transformer has an efficiency of 80 \% and works at 10 \mathrm{~V} and 4 \mathrm{~kW}. If the secondary voltage is 240 \mathrm{~V}, then the current in the secondary coil is :
Options:
A) 1.33 \mathrm{~A}
B) 13.33 \mathrm{~A}
C) 1.59 \mathrm{~A}
D) 15.1 \mathrm{~A}
68
EasyJEE Mains2024
A coil is places perpendicular to a magnetic field of $5000 \mathrm{~T}. When the field is changed to 3000 \mathrm{~T} in 2 \mathrm{~s}, an induced emf of 22 \mathrm{~V} is produced in the coil. If the diameter of the coil is 0.02 \mathrm{~m}$, then the number of turns in the coil is:
Options:
A) 35
B) 70
C) 7
D) 140
69
EasyJEE Mains2024
Match List I with List II List I List II (A) Gauss's law of magnetostatics (I) $\oint \vec{E} \cdot \vec{d} a=\frac{1}{\varepsilon_0} \int \rho d V (B) Faraday's law of electro magnetic induction (II) \oint \vec{B} \cdot \vec{d} a=0 (C) Ampere's law (III) \int \vec{E} \cdot \vec{d} l=\frac{-d}{d t} \int \vec{B} \cdot \vec{d} a (D) Gauss's law of electrostatics (IV) \oint \vec{B} \cdot \vec{d} l=\mu_0 I$ Choose the correct answer from the options given below:
Options:
A) A-III, B-IV, C-I, D-II
B) A-IV, B-II, C-III, D-I
C) A-II, B-III, C-IV, D-I
D) A-I, B-III, C-IV, D-II
70
EasyJEE Mains2024
Match List I with List II List - I List - II (A) $\oint \vec{B} \cdot \overrightarrow{d l}=\mu_o i_c+\mu_o \varepsilon_o \frac{d \phi_E}{d t} (I) Gauss' law for electricity (B) \oint \vec{E} \cdot \overrightarrow{d l}=\frac{d \phi_B}{d t} (II) Gauss' law for magnetism (C) \oint \vec{E} \cdot \overrightarrow{d A}=\frac{Q}{\varepsilon_o} (III) Faraday law (D) \oint \vec{B} \cdot \overrightarrow{d A}=0$ (IV) Ampere - Maxwell law Choose the correct answer from the options given below:
Options:
A) A-IV, B-III, C-I, D-II
B) A-I, B-II, C-III, D-IV
C) A-IV, B-I, C-III, D-II
D) A-II, B-III, C-I, D-IV
71
EasyJEE Mains2024
A rectangular loop of length $2.5 \mathrm{~m} and width 2 \mathrm{~m} is placed at 60^{\circ} to a magnetic field of 4 \mathrm{~T}. The loop is removed from the field in 10 \mathrm{~sec}$. The average emf induced in the loop during this time is
Options:
A) -2 \mathrm{~V}
B) +2 \mathrm{~V}
C) +1 \mathrm{~V}
D) -1 \mathrm{~V}
72
MediumJEE Mains2023
12 \mathrm{~V} battery connected to a coil of resistance 6 \Omega through a switch, drives a constant current in the circuit. The switch is opened in 1 \mathrm{~ms}. The emf induced across the coil is 20 \mathrm{~V}. The inductance of the coil is :
Options:
A) 5 ~ \mathrm{mH}
B) 8 ~\mathrm{mH}
C) 10~ \mathrm{mH}
D) 12 ~\mathrm{mH}
73
MediumJEE Mains2023
Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$ Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. Reason R: For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below
Options:
A) A is true but R is false
B) A is false but R is true
C) Both A and R are true but R is NOT the correct explanation of A
D) Both A and R are true and R is the correct explanation of A
74
MediumJEE Mains2023
Given below are two statements: Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double. Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Statement I is true but Statement II is false
B) Statement I is false but Statement II is true
C) Both Statement I and Statement II are false
D) Both Statement I and Statement II are true
75
EasyJEE Mains2023
An emf of $0.08 \mathrm{~V} is induced in a metal rod of length 10 \mathrm{~cm} held normal to a uniform magnetic field of 0.4 \mathrm{~T}$, when moves with a velocity of:
Options:
A) 20 \mathrm{~ms}^{-1}
B) 2 \mathrm{~ms}^{-1}
C) 3.2 \mathrm{~ms}^{-1}
D) 0.5 \mathrm{~ms}^{-1}
76
EasyJEE Mains2023
Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is
Options:
A) to bring the coil to rest quickly
B) to produce large deflecting torque on the coil
C) to oscillate the coil in magnetic field for longer period of time
D) to make the magnetic field radial
77
MediumJEE Mains2023
The induced emf can be produced in a coil by A. moving the coil with uniform speed inside uniform magnetic field B. moving the coil with non uniform speed inside uniform magnetic field C. rotating the coil inside the uniform magnetic field D. changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:
Options:
A) A and C only
B) C and D only
C) B and D only
D) B and C only
78
MediumJEE Mains2023
A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed : A. By changing the magnitude of the magnetic field within the coil. B. By changing the area of coil within the magnetic field. C. By changing the angle between the direction of magnetic field and the plane of the coil. D. By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below :
Options:
A) A, B and D only
B) A, B and C only
C) A and B only
D) A and C only
79
MediumJEE Mains2023
Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}
Options:
A) Metal ball will reach the earth's surface earlier than the insulating ball
B) Both will reach the earth's surface simultaneously.
C) Insulating ball will reach the earth's surface earlier than the metal ball
D) Time taken by them to reach the earth's surface will be independent of the properties of their materials
80
MediumJEE Mains2023
A square loop of area 25 cm$^2 has a resistance of 10 \Omega$. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1.0 sec, will be
Options:
A) \mathrm{1.0\times10^{-3}~J}
B) \mathrm{5\times10^{-3}~J}
C) \mathrm{2.5\times10^{-3}~J}
D) \mathrm{1.0\times10^{-4}~J}
81
MediumJEE Mains2023
Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$R' is placed inside a large square loop of wire of side L (L \gg R)$. The loops are coplanar and their centres coincide :
Options:
A) M=\frac{\sqrt{2} \mu_{0} R}{L^{2}}
B) M=\frac{2 \sqrt{2} \mu_{0} R}{L^{2}}
C) M=\frac{2 \sqrt{2} \mu_{0} R^{2}}{L}
D) M=\frac{\sqrt{2} \mu_{0} R^{2}}{L}
82
EasyJEE Mains2023
A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be __________.
Options:
A) 20 V
B) 8 V
C) 16 V
D) 12 V
83
EasyJEE Mains2023
A metallic rod of length 'L' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be :
Options:
A) \mathrm{\frac{1}{2}B^2L^2\omega}
B) \mathrm{\frac{1}{2}BL^2\omega}
C) \mathrm{\frac{1}{4}BL^2\omega}
D) \mathrm{\frac{1}{4}B^2L\omega}
84
EasyJEE Mains2023
A conducting circular loop of radius $\frac{10}{\sqrt\pi}$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is :
Options:
A) emf = 10 mV
B) emf = 5 mV
C) emf = 100 mV
D) emf = 1 mV
85
MediumJEE Mains2022
The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B2 at its centre. The ratio of ${{{B_2}} \over {{B_1}}}$ is
Options:
A) {5 \over 2}
B) {25 \over 4}
C) {5 \over 4}
D) {25 \over 2}
86
MediumJEE Mains2022
A small square loop of wire of side $l is placed inside a large square loop of wire \mathrm{L}(\mathrm{L}>>l). Both loops are coplanar and their centres coincide at point \mathrm{O}$ as shown in figure. The mutual inductance of the system is :
Options:
A) \frac{2 \sqrt{2} \mu_{0} \mathrm{~L}^{2}}{\pi l}
B) \frac{\mu_{0} l^{2}}{2 \sqrt{2} \pi \mathrm{L}}
C) \frac{2 \sqrt{2} \mu_{0} l^{2}}{\pi \mathrm{L}}
D)
\frac{\mu_{0} \mathrm{~L}^{2}}{2 \sqrt{2} \pi l}
87
MediumJEE Mains2022
A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be : (Assume the coil to be short circuited.)
Options:
A) Halved
B) Quadrupled
C) The same
D) Doubled
88
MediumJEE Mains2022
Two coils of self inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :
Options:
A) {1 \over {{L_1}}} + {1 \over {{L_2}}} + {1 \over M}
B) {L_1} + {L_2} + M
C) {L_1} + {L_2} + 2M
D) {L_1} + {L_2} - 2M
89
EasyJEE Mains2022
A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s$-1. If the horizontal component of earth's magnetic field is 0.2 \times 10-$4 T, then emf induced between the two ends of the conductor is :
Options:
A) 5 $\mu$V
B) 50 $\mu$V
C) 5 mV
D) 50 mv
90
MediumJEE Mains2022
The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi = (5{t^3} + 4{t^2} + 2t - 5)$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,
Options:
A) 15.6 A
B) 16.6 A
C) 17.6 A
D) 18.6 A
91
MediumJEE Mains2021
A square loop of side 20 cm and resistance 1$\Omega is moved towards right with a constant speed v0. The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4\Omega$. What should be the value of v0 so that a steady current of 2 mA flows in the loop?
Options:
A) 1 m/s
B) 1 cm/s
C) 102 m/s
D) 10$-$2 cm/s
92
MediumJEE Mains2021
A coil is placed in a magnetic field $\overrightarrow B as shown below :A current is induced in the coil because \overrightarrow B $ is :
Options:
A) Outward and decreasing with time
B) Parallel to the plane of coil and decreasing with time
C) Outward and increasing with time
D) Parallel to the plane of coil and increasing with time
93
MediumJEE Mains2021
A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is :
Options:
A) {{{\mu _0}} \over {4\pi }}8\sqrt 2 {{{a^2}} \over b}
B) {{{\mu _0}} \over {4\pi }}{{8\sqrt 2 } \over a}
C) {{{\mu _0}} \over {4\pi }}8\sqrt 2 {{{b^2}} \over a}
D) {{{\mu _0}} \over {4\pi }}{{8\sqrt 2 } \over b}
94
MediumJEE Mains2021
A constant magnetic field of 1T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a constant velocity of 1 m/s along the x-axis. At t = 0s, the centre of O of the ring is at x = $-$1m. What will be the value of the induced emf in the ring at t = 1s? (Assume the velocity of the ring does not change.)
Options:
A) 1V
B) 2$\pi$V
C) 2V
D) 0V
95
MediumJEE Mains2021
A bar magnet is passing through a conducting loop of radius R with velocity $\upsilon $. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve :
Options:
A)
B)
C)
D)
96
EasyJEE Mains2021
An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds :
Options:
A) 0.4
B) 0.8
C) 0.125
D) 0.2
97
MediumJEE Mains2021
The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance.
Options:
A) A-Flux, B-Power dissipated, C-EMF
B) A-Flux, B-EMF, C-Power dissipated
C) A-Power dissipated, B-Flux, C-EMF
D) A-EMF, B-Power dissipated, C-Flux
98
MediumJEE Mains2021
The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :
Options:
A) infinite
B) {L \over R}$ ln10
C) {L \over R}$ ln2
D) {L \over R}$ ln5
99
MediumJEE Mains2021
The magnetic field in a region is given by $\overrightarrow B = {B_o}\left( {{x \over a}} \right)\widehat k. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity \overrightarrow v = v0\widehat i$. The emf induced in the loop is :
Options:
A) {{{B_o}{v_o}{d^2}} \over {2a}}
B) {{{B_o}v_o^2d} \over {2a}}
C) {{{B_o}{v_o}d} \over {2a}}
D) {{{B_o}{v_o}{d^2}} \over a}
100
MediumJEE Mains2021
A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field $\overrightarrow B $ pointing into the page. An external agent pulls the bar to the left at a constant speed v.The correct statement about the directions of induced currents I1 and I2 flowing through R1 and R2 respectively is :
Options:
A) Both I1 and I2 are in clockwise direction
B) I1 is in clockwise direction and I2 is in anticlockwise direction
C) I1 is in anticlockwise direction and I2 is in clockwise direction
D) Both I1 and I2 are in anticlockwise direction
101
MediumJEE Mains2021
An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 $\times 10-4 Wb/m2 and the angle of dip is 60^\circ$. The emf induced between the tips of the plane wings will be __________.
Options:
A) 88.37 mV
B) 62.50 mV
C) 54.125 mV
D) 108.25 mV
102
EasyJEE Mains2021
Figure shows a circuit that contains four identical resistors with resistance R = 2.0$\Omega$, two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9V. The current 'i' just after the switch 'S' is closed will be :
Options:
A) 3.0 A
B) 3.37 A
C) 9 A
D) 2.25 A
103
MediumJEE Mains2020
An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length $l$ and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is :
Options:
A) {{{\mu _0}} \over {4\pi }}{{Ivl} \over {Rr}}
B) {{{\mu _0}} \over {\pi }}{{Ivl} \over {Rr}}
C) {{{\mu _0}} \over {2\pi }}{{Ivl} \over {Rr}}
D) {{2{\mu _0}} \over \pi }{{Ivl} \over {Rr}}
104
MediumJEE Mains2020
A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil? Three positions shown describe : (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit.
Options:
A)
B)
C)
D)
105
MediumJEE Mains2020
A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate ${{dB} \over {dt}} = 0.032 Ts–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 \times 10–8 \Omega $m)
Options:
A) 0.53 A
B) 0.43 A
C) 0.34 A
D) 0.61 A
106
MediumJEE Mains2020
An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency $\omega $, the average power loss in the loop due to Joule heating is :
Options:
A) {{\pi abB\omega } \over R}
B) {{{\pi ^2}{a^2}{b^2}{B^2}{\omega ^2}} \over R}
C) {{{\pi ^2}{a^2}{b^2}{B^2}{\omega ^2}} \over {2R}}
D) Zero
107
MediumJEE Mains2020
A shown in the figure, a battery of emf $\varepsilon $ is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = tc (tc is the time constant of the circuit) is :
Options:
A) {{\varepsilon L} \over {e{R^2}}}
B) {{\varepsilon L} \over {{R^2}}}
C) {{\varepsilon L} \over {{R^2}}}\left( {1 - {1 \over e}} \right)
D) {{\varepsilon R} \over {e{L^2}}}
108
MediumJEE Mains2020
At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loop is :
Options:
A) 48 μV
B) 28 μV
C) 56 μV
D) 36 μV
109
MediumJEE Mains2020
A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :
Options:
A) 2.5 s and 7.5 s
B) 5.0 s and 10.0 s
C) 5.0 s and 7.5 s
D) 2.5 s and 5.0 s
110
MediumJEE Mains2020
A long solenoid of radius R carries a time (t) - dependent current I(t)=I0t(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 (IR) and the induced EMF(VR) in the ring change as :
Options:
A) Direction of IR remains unchanged and VR is zero at t = 0.25
B) Direction of IR remains unchanged and VR is maximum at t = 0.5
C) At t = 0.25 direction of IR reverses and VR is maximum
D) At t = 0.5 direction of IR reverses and VR is zero
111
MediumJEE Mains2020
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?
Options:
A) \phi i = \phi $0
B) \phi i < \phi $0
C) \phi i > \phi $0
D) \phi i = - \phi $0
112
MediumJEE Mains2019
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 1 cm s-1. At some instant, a part of L is in a uniform magnetic field of 1 T, 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 :
Options:
A) 115 $\mu $A
B) 170 $\mu $A
C) 60 $\mu $A
D) 150 $\mu $A
113
MediumJEE Mains2019
A very long solenoid of radius R is carrying current I(t) = kte–at(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 :-
Options:
A)
B)
C)
D)
114
MediumJEE Mains2019
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 :-
Options:
A) 3.67 × 10–4 Wb
B) 3.67 × 10–3 Wb
C) 6.67 × 10–4 Wb
D) 6.67 × 10–3 Wb
115
MediumJEE Mains2019
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 :
Options:
A) 1/L2
B) 1/L
C) L
D) L2
116
MediumJEE Mains2019
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 :
Options:
A) {2 \over {\ln 2}}
B) {\ln 2}
C) 2{\ln 2}
D) {1 \over 2}{\ln 2}
117
MediumJEE Mains2019
A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms–1, at right angles to the horizontal component of the earth's magnetic field of 0.3 $ \times $ 10–4 Wb/m2. The value of the induced emf in wire is :
Options:
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
118
MediumJEE Mains2019
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:
Options:
A) decreases by a factor of $9\sqrt 3
B) increases by a factor of 27
C) decreases by a factor of 9
D) increases by a factor of 3
119
MediumJEE Mains2019
There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is :
Options:
A) {{{n_2}} \over {{n_1}}}.{{{r_2}^2} \over {{r_1}^2}}
B) {{{n_2}} \over {{n_1}}}
C) {{{n_1}} \over {{n_2}}}
D) {{{n_2}} \over {{n_1}}}.{{{r_1}} \over {{r_2}}}
120
MediumJEE Mains2019
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 -
Options:
A) 740 J
B) 637.5 J
C) 540 J
D) 437.5 J
121
MediumJEE Mains2019
A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is -
Options:
A) 2mV
B) 12 mV
C) 6 mV
D) 1 mV
122
MediumJEE Mains2019
A conducting circular loop made of a thin wire, has area 3.5 $ \times 10-3 m2 and resistance 10 \Omega . It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50\pi $t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to :
Options:
A) 0.14 mC
B) 0.7 mC
C) 0.21 mC
D) 0.6 mC
123
MediumJEE Mains2018
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 maxium e.m.f. induced in the coil will be:
Options:
A) 3 nBA$\omega
B) {3 \over 2} nBA\omega
C) nBA$\omega
D) {1 \over 2} nBA\omega
124
MediumJEE Mains2018
At the center 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 their smaller coil after a time t of its start of rotation.
Options:
A) {{{\mu _o}{\rm I}} \over {2\,R}} \omega \pi r2 sin\omega $ t
B) {{{\mu _o}{\rm I}} \over {4\,R}} \omega \pi r2 sin\omega $ t
C) {{{\mu _o}{\rm I}} \over {4\,R}} \omega r2 sin\omega $ t
D) {{{\mu _o}{\rm I}} \over {2\,R}} \omega r2 sin\omega $ t
125
MediumJEE Mains2018
A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l 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 igure. The terminal speed of the copper rod is :
Options:
A) {{mg\,R\,\tan \,\theta } \over {{B^2}\,{l^2}}}
B) {{mg\,R\,\cot \,\theta } \over {{B^2}\,{l^2}}}
C) {{mg\,R\,\sin \,\theta } \over {{B^2}\,{l^2}}}
D) {{mg\,R\,\cos \,\theta } \over {{B^2}\,{l^2}}}
126
MediumJEE Mains2017
A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium ?
Options:
A)
B)
C)
D)
127
MediumJEE Mains2017
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 = Io cos ($\omega $t). The emf induced in the smaller inner loop is nearly :
Options:
A) {{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \sin \left( {\omega t} \right)
B) {{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \cos \left( {\omega t} \right)
C) \pi {\mu _o}{I_o}\,{{{a^2}} \over b}\omega \sin \left( {\omega t} \right)
D) {{\pi {\mu _o}{I_o}\,{b^2}} \over a}\omega \cos \left( {\omega t} \right)
128
MediumJEE Mains2017
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:
Options:
A) 275 Wb
B) 200 Wb
C) 225 Wb
D) 250 Wb
129
MediumJEE Mains2016
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) :
Options:
A) \sigma 1 = \in 0 \upsilon B, \sigma 2 = - \in 0 \upsilon $ B
B) \sigma 1 = {{{ \in _0}\upsilon \,B} \over 2}, \sigma 2 = {{ - { \in _0}\,\upsilon B} \over 2}
C) \sigma 1 = \sigma 2 = { \in _0}\,\upsilon B
D) \sigma 1 = {{ - { \in _0}\upsilon B} \over 2}, \sigma 2 = {{ { \in _0}\upsilon B} \over 2},
130
MediumJEE Mains2016
A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as B = B0e${^{{{ - t} \over r}}} , where B0 and \tau are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time (t \to \infty $) is :
Options:
A) {{{\pi ^2}{r^4}B_0^4} \over {2\tau R}}
B) {{{\pi ^2}{r^4}B_0^2} \over {2\tau R}}
C) {{{\pi ^2}{r^4}B_0^2R} \over \tau }
D) {{{\pi ^2}{r^4}B_0^2} \over {\tau R}}
131
MediumJEE Mains2015
Two coaxial solenoids of different radius carry current $I in the same direction. \overrightarrow {{F_1}} be the magnetic force on the inner solenoid due to the outer one and \overrightarrow {{F_2}} $ be the magnetic force on the outer solenoid due to the inner one. Then :
Options:
A) \overrightarrow {{F_1}} is radially in wards and \overrightarrow {{F_2}} = 0
B) \overrightarrow {{F_1}} is radially outwards and \overrightarrow {{F_2}} = 0
C) \overrightarrow {{F_1}} = \overrightarrow {{F_2}} = 0
D) \overrightarrow {{F_1}} is radially inwards and \overrightarrow {{F_2}} $ is radially outards
132
MediumJEE Mains2013
A circular loop of radius $0.3 cm lies center of the small loop is on the axis of the bigger loop. The distance between their centers is 15 cm. If a current of 2.0 A$ flows through the smaller loop, than the flux linked with bigger loop is
Options:
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
133
MediumJEE Mains2013
A metallic rod of length $'\ell ' is tied to a string of length 2\ell and made to rotate with angular speed w on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f$ induced across the ends of the rod is
Options:
A) {{2B\omega \ell } \over 2}
B) {{3B\omega \ell } \over 2}
C) {{4B\omega {\ell ^2}} \over 2}
D) {{5B\omega {\ell ^2}} \over 2}
134
MediumJEE Mains2012
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 :
Options:
A) development 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 para-magnetic material.
D) electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.
135
MediumJEE Mains2011
A boat is moving due east in a region where the earth's magnetic fields is $5.0 \times {10^{ - 5}} N{A^{ - 1}}\,{m^{ - 1}} due north and horizontal. The best carries a vertical aerial 2 m long. If the speed of the boat is 1.50\,m{s^{ - 1}}, the magnitude of the induced emf$ in the wire of aerial is :
Options:
A) 0.75 mV
B) 0.50 mV
C) 0.15 mV
D) 1 mV
136
MediumJEE Mains2010
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
Options:
A) {I_1} = - {I_2} = {{Blv} \over {6R}},\,\,I = {{2Blv} \over {6R}}
B) {I_1} = {I_2} = {{Blv} \over {3R}},\,\,I = {{2Blv} \over {3R}}
C) {I_1} = {I_2} = I = {{Blv} \over R}
D) {I_1} = {I_2} = {{Blv} \over {6R}},I = {{Blv} \over {3R}}
137
MediumJEE Mains2008
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 solenoid has 300 turns and the other 400 turns, their mutual inductance is \left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,Tm\,{A^{ - 1}}} \right)
Options:
A) 2.4\pi \times {10^{ - 5}}H
B) 4.8\pi \times {10^{ - 4}}H
C) 4.8\pi \times {10^{ - 5}}H
D) 2.4\pi \times {10^{ - 4}}H
138
MediumJEE Mains2007
An ideal coil of $10H is connected in series with a resistance of 5\Omega and a battery of 5V. 2$ second after the connection is made, the current flowing in ampere in the circuit is
Options:
A) \left( {1 - {e^{ - 1}}} \right)
B) \left( {1 - e} \right)
C) e
D) {{e^{ - 1}}}
139
MediumJEE Mains2006
Which of the following units denotes the dimension ${{M{L^2}} \over {{Q^2}}}, where Q$ denotes the electric charge?
Options:
A) Wb/{m^2}
B) Henry $(H)
C) H/{m^2}
D) Weber $(Wb)
140
MediumJEE Mains2006
The flux linked with a coil at any instant $'t' is given by \phi = 10{t^2} - 50t + 250 The induced emf at t=3s$ is
Options:
A) -190 V
B) -10 V
C) 10 V
D) 190 V
141
MediumJEE Mains2006
An inductor $(L=100 mH), a resistor \left( {R = 100\,\Omega } \right) and a battery \left( {E = 100V} \right) are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms$ after the short circuit is
Options:
A) 1/eA
B) eA
C) 0.1 A
D) 1 A
142
MediumJEE Mains2005
A coil of inductance $300 mH and resistance 2\,\Omega is connected to a source of voltage 2 V$. The current reaches half of its steady state value in
Options:
A) 0.1 s
B) 0.05 s
C) 0.3 s
D) 0.15 s
143
MediumJEE Mains2005
One conducting $U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v, then the emf induced in the circuit in terms of B,l and v where l$ is the width of each tube, will be
Options:
A) -Blv
B) blv
C) 2 Blv
D) zero
144
MediumJEE Mains2004
A metal conductor of length $1 m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth's magnetic field is 0.2 \times {10^{ - 4}}T, then the e.m.f.$ developed between the two ends of the conductor is
Options:
A) 5mV
B) 50\mu V
C) 5\mu V
D) 50mV
145
MediumJEE Mains2004
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
Options:
A) {{\left( {{W_2} - {W_1}} \right)} \over {Rnt}}
B) - {{n\left( {{W_2} - {W_1}} \right)} \over {5\,\,Rt}}
C) - {{\left( {{W_2} - {W_1}} \right)} \over {5\,\,Rnt}}
D) - {{n\left( {{W_2} - {W_1}} \right)} \over {Rt}}
146
MediumJEE Mains2004
In a uniform magnetic field of induction $B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with an angular frequency \omega . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R,$ the mean power generated per period of rotation is
Options:
A) {{{{\left( {B\pi r\omega } \right)}^2}} \over {2R}}
B) {{{{\left( {B\pi {r^2}\omega } \right)}^2}} \over {8R}}
C) {{B\pi {r^2}\omega } \over {2R}}
D) {{{{\left( {B\pi r{\omega ^2}} \right)}^2}} \over {8R}}
147
MediumJEE Mains2003
When the current changes from $ + 2A to -2A in 0.05 second, an e.m.f. of 8 V$ is inducted in a coil. The coefficient of self- induction of the coil is
Options:
A) 0.2H
B) 0.4H
C) 0.8 H
D) 0.1 H
148
MediumJEE Mains2003
Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
Options:
A) the rates at which currents are changing in the two coils
B) relative position and orientation of the two coils
C) the currents in the two coils
D) the materials of the wires of the coils
149
MediumJEE Mains2002
A conducting square loop of side $L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced emf$ is
Options:
A) zero
B) RvB
C) vBL/R
D) vBL
150
MediumJEE Mains2002
The inductance between $A and D$ is
Options:
A) 3.66 H
B) 9 H
C) 0.66 H
D) 1 H
151
MediumJEE Mains2026
A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T . The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of 60^{\circ} with vertical, then maximum induced EMF between the point of suspension and point of oscillation is \_\_\_\_ mV . (Take \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
152
MediumJEE Mains2026
A conducting circular loop is rotated about its diameter at a constant angular speed of 100 \mathrm{rad} / \mathrm{s} in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by 30^{\circ} from the horizontal position, the induced EMF is 15.4 mV . The radius of the loop is \_\_\_\_ mm. $ \left(\text { Take } \pi=\frac{22}{7}\right)
Options:
153
MediumJEE Mains2026
Inductance of a coil with 10^4 turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10 \Omega. The energy density in the inductor when the current reaches \left(\frac{1}{e}\right) of its maximum value is \alpha \pi \times \frac{1}{e^2} \mathrm{~J} / \mathrm{m}^3. The value of \alpha is \_\_\_\_ . $ \left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}\right) .
Options:
154
MediumJEE Mains2025
Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of \frac{1}{\sqrt{2}} Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 \mathrm{~cm} / \mathrm{s}, induced emf between points A and E is ________ mV .
Options:
155
MediumJEE Mains2025
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E ∝ tn, then value of n is _________.
Options:
156
EasyJEE Mains2025
In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 \mathrm{~A} / \mathrm{s}. At an instant when R is 12 \Omega, the value of the current in the circuit will be ________ A.
Options:
157
EasyJEE Mains2024
The current in an inductor is given by $\mathrm{I}=(3 \mathrm{t}+8) where \mathrm{t} is in second. The magnitude of induced emf produced in the inductor is 12 \mathrm{~mV}. The self-inductance of the inductor _________ \mathrm{mH}$.
Options:
158
EasyJEE Mains2024
A coil of 200 turns and area 0.20 \mathrm{~m}^2 is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 \mathrm{~T} perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \frac{2 \pi}{\beta} volt. The value of \beta is _______.
Options:
159
HardJEE Mains2024
A rectangular loop of sides 12 \mathrm{~cm} and 5 \mathrm{~cm}, with its sides parallel to the x-axis and y-axis respectively, moves with a velocity of 5 \mathrm{~cm} / \mathrm{s} in the positive x axis direction, in a space containing a variable magnetic field in the positive z direction. The field has a gradient of 10^{-3} \mathrm{~T} / \mathrm{cm} along the negative x direction and it is decreasing with time at the rate of 10^{-3} \mathrm{~T} / \mathrm{s}. If the resistance of the loop is 6 \mathrm{~m} \Omega, the power dissipated by the loop as heat is __________ \times 10^{-9} \mathrm{~W}.
Options:
160
EasyJEE Mains2024
The magnetic flux $\phi (in weber) linked with a closed circuit of resistance 8 \Omega varies with time (in seconds) as \phi=5 t^2-36 t+1. The induced current in the circuit at t=2 \mathrm{~s}$ is __________ A.
Options:
161
MediumJEE Mains2024
A small square loop of wire of side $l is placed inside a large square loop of wire of side L\left(L=l^2\right). The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is \sqrt{x} \times 10^{-7} \mathrm{H}, where x=$ _________.
Options:
162
MediumJEE Mains2024
A ceiling fan having 3 blades of length $80 \mathrm{~cm} each is rotating with an angular velocity of 1200 \mathrm{rpm}. The magnetic field of earth in that region is 0.5 \mathrm{G} and angle of dip is 30^{\circ}. The emf induced across the blades is \mathrm{N} \pi \times 10^{-5} \mathrm{~V}. The value of \mathrm{N}$ is _________.
Options:
163
EasyJEE Mains2024
A horizontal straight wire $5 \mathrm{~m} long extending from east to west falling freely at right angle to horizontal component of earths magnetic field 0.60 \times 10^{-4} \mathrm{~Wbm}^{-2}. The instantaneous value of emf induced in the wire when its velocity is 10 \mathrm{~ms}^{-1} is _________ \times 10^{-3} \mathrm{~V}$.
Options:
164
MediumJEE Mains2024
A square loop of side $10 \mathrm{~cm} and resistance 0.7 \Omega is placed vertically in east-west plane. A uniform magnetic field of 0.20 T is set up across the plane in north east direction. The magnetic field is decreased to zero in 1 \mathrm{~s} at a steady rate. Then, magnitude of induced emf is \sqrt{x} \times 10^{-3} \mathrm{~V}. The value of x$ is __________.
Options:
165
EasyJEE Mains2024
Two coils have mutual inductance $0.002 \mathrm{~H}. The current changes in the first coil according to the relation \mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}, where \mathrm{i}_0=5 \mathrm{~A} and \omega=50 \pi rad/s. The maximum value of emf in the second coil is \frac{\pi}{\alpha} \mathrm{~V}. The value of \alpha$ is _______.
Options:
166
MediumJEE Mains2023
A 20 \mathrm{~cm} long metallic rod is rotated with 210~ \mathrm{rpm} about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field 0.2 \mathrm{~T} parallel to the axis exists everywhere. The emf developed between the centre and the ring is ____________ \mathrm{mV}. Take \pi=\frac{22}{7}
Options:
167
MediumJEE Mains2023
An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $24 \mathrm{~cm}^{2}. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12 ~\Omega. If an externally applied uniform magnetic field in the core along its axis changes from 1.5 \mathrm{~T} in one direction to 1.5 ~\mathrm{T} in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ \mathrm{mC}$.
Options:
168
MediumJEE Mains2023
A conducting circular loop is placed in a uniform magnetic field of $0.4 \mathrm{~T} with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 \mathrm{~mm} / \mathrm{s}. The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 \mathrm{~cm} will be ___________ \mu \mathrm{V}$.
Options:
169
EasyJEE Mains2023
A metallic cube of side $15 \mathrm{~cm} moving along y-axis at a uniform velocity of 2 \mathrm{~ms}^{-1}. In a region of uniform magnetic field of magnitude 0.5 \mathrm{~T} directed along z$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.
Options:
170
EasyJEE Mains2023
The magnetic field B crossing normally a square metallic plate of area $4 \mathrm{~m}^{2} is changing with time as shown in figure. The magnitude of induced emf in the plate during \mathrm{t}=2 s to \mathrm{t}=4 s, is __________ \mathrm{mV}$.
Options:
171
MediumJEE Mains2023
A square loop of side $2.0 \mathrm{~cm} is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 \mathrm{~A} and angular frequency 700 ~\mathrm{rad} ~\mathrm{s}^{-1}. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is x \times 10^{-4} \mathrm{~V}. The value of x is __________. \text { (Take, } \pi=\frac{22}{7} \text { ) }
Options:
172
MediumJEE Mains2023
A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5$\Omega, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be ____________ 10^{-3}$ N.
Options:
173
MediumJEE Mains2023
Two concentric circular coils with radii $1 \mathrm{~cm} and 1000 \mathrm{~cm}, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ \times 10^{-8} \mathrm{H}. (Take, \pi^{2}=10$ )
Options:
174
MediumJEE Mains2023
As per the given figure, if $\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / s then the value of \mathrm{V}_{\mathrm{AB}} at this instant will be ____________ \mathrm{V}$.
Options:
175
EasyJEE Mains2023
A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cms$^{-1}$. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be __________ mV.
Options:
176
EasyJEE Mains2023
Three identical resistors with resistance R = 12$\Omega$ and two identical inductors with self inductance L = 5 mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _____________ A.
Options:
177
EasyJEE Mains2022
For the given circuit the current through battery of 6 V just after closing the switch 'S' will be _________ A.
Options:
178
MediumJEE Mains2022
A conducting circular loop is placed in $X-Y plane in presence of magnetic field \overrightarrow{\mathrm{B}}=\left(3 \mathrm{t}^{3} \,\hat{j}+3 \mathrm{t}^{2}\, \hat{k}\right) in SI unit. If the radius of the loop is 1 \mathrm{~m}, the induced emf in the loop, at time, \mathrm{t}=2 \mathrm{~s} is \mathrm{n} \pi \,\mathrm{V}. The value of \mathrm{n}$ is ___________.
Options:
179
MediumJEE Mains2022
In a coil of resistance $8 \,\Omega, the magnetic flux due to an external magnetic field varies with time as \phi=\frac{2}{3}\left(9-t^{2}\right). The value of total heat produced in the coil, till the flux becomes zero, will be _____________ J$.
Options:
180
EasyJEE Mains2022
Magnetic flux (in weber) in a closed circuit of resistance 20 $\Omega varies with time t(s) at \phi = 8t2 -$ 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.
Options:
181
EasyJEE Mains2022
A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is 4 $\times 10-3 T and the angle of dip is 45^\circ$. The emf induced in the rod is ___________ mV.
Options:
182
EasyJEE Mains2022
A 10 $\Omega, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 \mu$s. The average e.m.f. induced in the coil is ____________ V.
Options:
183
EasyJEE Mains2022
The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t2) A. The amount of energy spent during the period when current changes from 0 to 2 A is ____________ J.
Options:
184
EasyJEE Mains2022
A circular coil of 1000 turns each with area 1m2 is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ___________ V.
Options:
185
MediumJEE Mains2021
If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ...............[mp = 1.67 $\times 10-27 kg, e = 1.6 \times 10-19C, Speed of light = 3 \times$ 108 m/s]
Options:
186
EasyJEE Mains2021
A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s$-1 in a uniform horizontal magnetic field of 3.0 \times 10-2 T. The maximum emf induced the coil will be ................. \times 10-$2 volt (rounded off to the nearest integer)
Options:
187
EasyJEE Mains2021
In the given figure the magnetic flux through the loop increases according to the relation $\phiB(t) = 10t2 + 20t, where \phiB is in milliwebers and t is in seconds. The magnitude of current through R = 2\Omega$ resistor at t = 5 s is ___________ mA.
Options:
188
MediumJEE Mains2021
A circular conducting coil of radius 1 m is being heated by the change of magnetic field $\overrightarrow B passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2 \mu\Omega. The magnetic field is slowly switched off such that its magnitude changes in time as B = {4 \over \pi } \times {10^{ - 3}}T\left( {1 - {t \over {100}}} \right)$The energy dissipated by the coil before the magnetic field is switched off completely is E = ___________ mJ.
Options:
189
MediumJEE Mains2021
A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______J.
Options:
190
MediumJEE Mains2020
A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1A and it is decreasing at a rate of 102 A s–1. The value of the potential difference VP – VQ , (in volts) at that instant, is _________.
Options:
191
MediumJEE Mains2020
Two concentric circular coils, C1 and C2 are placed in the XY plane. C1 has 500 turns, and a radius of 1 cm. C2 has 200 turns and radius of 20 cm. C2 carries a time dependent current I(t) = (5t2 – 2t + 3) A where t is in s. The emf induced in C1 (in mV), at the instant t = 1 s is ${4 \over x}$. The value of x is ___ .
Options:
192
MediumJEE Mains2020
A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 $ \times 10–5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in \mu $V) in the coil will be close to the integer _______.
Options:
193
MediumJEE Mains2020
In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ________.
Options:
194
MediumJEE Mains2020
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 $\overrightarrow B = \left( {3\widehat i + 4\widehat k} \right)T$ . The quantity of flux through the loop ABCDEFA (in Wb) is _______.
Options:
195
MediumMHT CET2025
Two inductors of 80 mH each are joined in parallel. The current passing through the combination is 2.1 A . The energy stored in this combination of inductors is
Options:
A) 4.84 \times 10^{-2} \mathrm{~J}
B) 7.26 \times 10^{-2} \mathrm{~J}
C) 8.82 \times 10^{-2} \mathrm{~J}
D) 10.85 \times 10^{-2} \mathrm{~J}
196
MediumMHT CET2025
A coil of effective area 3 \mathrm{~m}^2 is placed at right angles to a magnetic field of induction 0.05 \mathrm{~Wb} / \mathrm{m}^2 If the field is decreased to 20 \% of its original value in 10 second, the e.m.f. induced in the coil will be
Options:
A) 10 mV
B) 12 mV
C) 15 mV
D) 20 mV
197
MediumMHT CET2025
A coil having ' N ' turns and resistance ' R ' \Omega is connected to a galvanometer of resistance ' 6 R ' \Omega. The magnetic flux linked with this coil changes from \phi_1 weber to \phi_2 weber in time ' t ' second. The induced current in the circuit is
Options:
A) \frac{\mathrm{N}\left(\phi_2-\phi_1\right)}{\mathrm{t}}
B) \frac{N\left(\phi_2-\phi_1\right)}{7 R t}
C) \frac{\mathrm{N}\left(\phi_2-\phi_1\right)}{\mathrm{Rt}}
D) \frac{N\left(\phi_2-\phi_1\right)}{6 R t}
198
MediumMHT CET2025
The plot of magnetic flux ' \phi ' linked with the coil versus current ' I ' is as shown in figure for two inductors \mathrm{L}_1 and \mathrm{L}_2. The self inductance of
Options:
A) \quad \mathrm{L}_1 is equal to that of \mathrm{L}_2.
B) \quad \mathrm{L}_1 is less than that of \mathrm{L}_2.
C) \quad \mathrm{L}_1 is greater than that of \mathrm{L}_2.
D) \quad \mathrm{L}_1 is half that of \mathrm{L}_2.
199
MediumMHT CET2025
A long rectangular conducting loop of width ' l ', mass ' m ' and resistance ' R ' is placed partly in a perpendicular magnetic field ' B '. It is pushed downwards with velocity ' V ' so that it may continue to fall freely. The velocity ' V ' is
Options:
A) \frac{\mathrm{mgR}^2}{\mathrm{~B} l}
B) \frac{\mathrm{B}^2 l^2 \mathrm{R}}{\mathrm{mg}}
C) \frac{\mathrm{mgR}}{\mathrm{B}^2 l^2}
D) \frac{\mathrm{mgl}}{\mathrm{B}^2 \mathrm{R}^2}
200
MediumMHT CET2025
Two coils P and Q are kept near each other. When no current flows through coil P and current increases in coil Q at the rate 10 \mathrm{~A} / \mathrm{s}, the emf in coil P is 12 mV . When coil Q carries no current and current of 1.5 A flows through coil P , the magnetic flux linked with the coil Q in mWb is
Options:
A) 0.9
B) 1.2
C) 1.5
D) 1.8
201
MediumMHT CET2025
When magnetic flux changes from 6.5 \times 10^{-2} \mathrm{~Wb} to 11 \times 10^{-2} \mathrm{~Wb} and the change in current is 0.03 A , the coefficient of mutual inductance will be
Options:
A) 1.0 H
B) 1.2 H
C) 1.5 H
D) 1.8 H
202
MediumMHT CET2025
Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively \mathrm{L}_{\mathrm{A}}=10 \mathrm{H} and \mathrm{L}_{\mathrm{B}}=10 \mathrm{mH}. The total resistance of each circuit is 40 \Omega. The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is
Options:
A) 800
B) 1000
C) 1200
D) 1400
203
MediumMHT CET2025
A magnetic field 4 \times 10^{-2} \mathrm{~T} acts at right angles to a coil of area 100 \mathrm{~cm}^2 with 50 turns. The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time ' t '. The value of ' t ' is
Options:
A) 0.02 second
B) 0.05 second
C) 0.2 second
D) 2 second
204
MediumMHT CET2025
A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ( \mathrm{g}= acceleration due to gravity)
Options:
A) g
B) less than g
C) more than g
D) zero
205
MediumMHT CET2025
A coil of wire of radius ' r ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns is
Options:
A) 80 mH
B) 75 mH
C) 108 mH
D) 90 mH
206
MediumMHT CET2025
A coil of ' n ' turns and resistance R \Omega is connected in series with a resistance \frac{R}{2}. The combination is moved for time ' t ' second through magnetic flux \phi_1 to \phi_2. The induced current in the circuit is
Options:
A) \frac{n\left(\phi_1-\phi_2\right)}{3 R t}
B) \frac{2 n\left(\phi_1-\phi_2\right)}{3 R t}
C) \frac{2 n\left(\phi_1-\phi_2\right)}{R t}
D) \frac{\mathrm{n}\left(\phi_1-\phi_2\right)}{\mathrm{Rt}}
207
MediumMHT CET2025
The equivalent inductance between A and B is equal to
Options:
A) \frac{4}{5} \mathrm{H}
B) \frac{5}{4} \mathrm{H}
C) \frac{3}{10} \mathrm{H}
D) 15 H
208
MediumMHT CET2025
A coil of ' n ' turns and area ' A ' is suddenly removed from a magnetic field, a charge ' q ' flows through the coil. If resistance of the coil is ' R ' then the magnetic flux density is (in \mathrm{Wb} / \mathrm{m}^2 )
Options:
A) \frac{q^2 R}{2 n A}
B) \frac{q R}{n A}
C) \frac{q R^2}{n A}
D) \frac{q R}{2 n A}
209
MediumMHT CET2025
A coil of n turns and resistance \mathrm{R} \Omega is connected in series with resistance R / 4. The combination is moved for time t second through magnetic flux \phi to \phi_2. The induced current in the circuit is
Options:
A) \frac{2 n\left(\phi_1-\phi_2\right)}{5 R t}
B) \frac{4 n\left(\phi_1-\phi_2\right)}{5 R t}
C) \frac{3 n\left(\phi_1-\phi_2\right)}{4 R t}
D) \frac{5 n\left(\phi_1-\phi_2\right)}{3 R t}
210
MediumMHT CET2025
Two identical coils of inductance L joined in series are placed very close to each other such that the winding direction of one coil is exactly opposite to that of the other. The net inductance is
Options:
A) \frac{\mathrm{L}}{2}
B) 2 L
C) zero
D) L
211
MediumMHT CET2025
When a current in the conducting coil is changed from 5 A in one direction to 5 A in opposite direction in 0.5 second, an average induced e.m.f in the coil is 2 V . The selfinductance of the coil is
Options:
A) 25 mH
B) 50 mH
C) 75 mH
D) 100 mH
212
MediumMHT CET2025
Figure shows the north pole of a magnet moving away from a thick conducting loop containing a capacitor. The excess positive charge will arrive on
Options:
A) plate ' a '
B) plate ' b '
C) both plates 'a' and 'b'
D) neither plate ' a ' nor plate ' b '
213
MediumMHT CET2025
A graph of magnetic flux (\phi) versus current (I) is shown for four inductors \mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}. The largest value of self-inductance is for inductor
Options:
A) R
B) P
C) Q
D) S
214
MediumMHT CET2025
The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on
Options:
A) initial magnetic flux only.
B) final magnetic flux only.
C) the total change in magnetic flux.
D) the rate of change of magnetic flux.
215
MediumMHT CET2025
A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet while it is passing through the ring is
Options:
A) more than acceleration due to gravity.
B) less than acceleration due to gravity.
C) depends on the diameter of ring and length of magnet.
D) depends on pole strength of magnet.
216
MediumMHT CET2025
A coil of resistance 400 \Omega is placed in { }^3 magnetic field. If the magnetic flux ' \phi, ( Wb ) linked with the coil varies with time ' t ' ( s ) { }^{\text {is }} \phi=50 \mathrm{t}^2+4, the current in the coil at \mathrm{t}=2 \mathrm{~s} will be
Options:
A) 1 A
B) 2 A
C) 0.5 A
D) 0.1 A
217
MediumMHT CET2025
A coil is wound on a core of rectangular crosssection. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the selfinductance increases by a factor
Options:
A) \frac{1}{6}
B) 1
C) 3
D) 27
218
MediumMHT CET2025
A conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then
Options:
A) induced current in the coil is zero.
B) induced current in the coil is anticlockwise.
C) induced current in the coil is clockwise.
D) ring will come to rest.
219
MediumMHT CET2025
What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?
Options:
A) \pi
B) -\frac{\pi}{6}
C) \frac{\pi}{3}
D) \frac{\pi}{2}
220
MediumMHT CET2025
Two coils P and Q are kept near each other. When no current flows through coil P and current increases in coil Q at the rate of 10 \mathrm{~A} / \mathrm{S}, the e.m.f. in coil P is 15 mV . When coil Q carries no current and current of 1.8 A flows through coil P, the magnetic flux linked with coil Q is
Options:
A) 1.8 mWb
B) 2.7 mWb
C) 1.5 mWb
D) 1 mWb
221
MediumMHT CET2025
To manufacture a solenoid of length ' l ' and inductance ' L ', the length of the thin wire required is (Diameter of the solenoid is very less than length, \mu_0= permeability of free space)
Options:
A) \left[\frac{4 \pi l L}{\mu_0}\right]^{\frac{1}{2}}
B) \left[\frac{2 \pi l}{\mu_0 \mathrm{~L}}\right]^{\frac{1}{2}}
C) \left[\frac{4 \pi \mu_0}{l \mathrm{~L}}\right]^{\frac{1}{2}}
D) \left[\frac{2 \pi \mu_0 \mathrm{~L}}{l}\right]^{\frac{1}{2}}
222
MediumMHT CET2025
Initially a rectangular coil with length vertical is moving out with constant velocity ' v ' in a constant magnetic field ' B ' towards right. Now the same coil is rotated through 90^{\circ} in same plane in same magnetic field B and the coil is moving with same velocity \mathbf{v}. The magnitude of induced e.m.f. is now
Options:
A) greater than initial induced e.m.f.
B) less than initial induced e.m.f.
C) equal to initial induced e.m.f.
D) sometimes greater and sometimes less than initial induced e.m.f.
223
MediumMHT CET2025
A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle \theta. The component of earth's magnetic field in the direction perpendicular to swing is B . Maximum e.m.f. induced across the pendulum is ( \mathrm{g}= acceleration due to gravity)
Options:
A) 2 \mathrm{BL}(\sqrt{\mathrm{gL}})\left(\sin \frac{\theta}{2}\right)
B) \mathrm{BL}(\sqrt{\mathrm{gL}})\left(\sin \frac{\theta}{2}\right)
C) \mathrm{BL}(\sqrt{\mathrm{gL}})^2\left(\sin \frac{\theta}{2}\right)
D) 2 \mathrm{BL}(\sqrt{\mathrm{gL}})\left(\sin ^2 \frac{\theta}{2}\right)
224
MediumMHT CET2025
Three inductances are connected as shown in the figure. The equivalent inductance between A and b is
Options:
A) 2.25 H
B) 1.20 H
C) 0.225 H
D) 0.120 H
225
MediumMHT CET2025
The current flowing through an inductor of selfinductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses \mathrm{dI} / \mathrm{dt} is shown graphically by figure
Options:
A) B
B) A
C) D
D) C
226
MediumMHT CET2025
The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV . Current in the primary is reduced from 6 A to 3 A . The time required for the change of current is
Options:
A) 4 \times 10^{-3} \mathrm{~s}
B) 6 \times 10^{-3} \mathrm{~s}
C) 2 \times 10^{-3} \mathrm{~s}
D) 3 \times 10^{-3} \mathrm{~s}
227
MediumMHT CET2025
Two planar concentric rings of metal wire having radii \mathrm{r}_1 and \mathrm{r}_2\left(\mathrm{r}_1>\mathrm{r}_2\right) are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( \mu_0= permeability of free space)
Options:
A) \frac{\mu_0 \pi r_1^2}{2 r_2}
B) \frac{\mu_0 \pi r_1^2}{2 r_1}
C) \frac{\mu_0 \pi\left(r_1+r_2\right)^2}{2 r_1}
D) \frac{\mu_0 \pi\left(r_1-r_2\right)^2}{2 r_2}
228
MediumMHT CET2025
Out of the following which law obeys the law of conservation of energy?
Options:
A) Kirchhoff's 1^{\text {st }} law in electricity.
B) Lenz's law in induction.
C) Ampere's circuital law.
D) Gauss's law in electrostatics.
229
MediumMHT CET2025
The magnetic flux through a coil is 4 \times 10^{-4} \mathrm{~Wb} at time t=0. It reduces to 30 \% of its original value in time t second. If e.m.f. induced in the coil is 0.56 mV then the value of t is
Options:
A) 0.5 s
B) \quad 0.4 \mathrm{~s}
C) 0.8 s
D) 0.7 s
230
MediumMHT CET2025
When three inductors of same inductance ' L ' are connected in series and ' I ' is the current passing through the circuit. The energy stored in the circuit is
Options:
A) \frac{1}{2} \mathrm{LI}^2
B) \frac{3}{2} \mathrm{LI}^2
C) \frac{5}{2} \mathrm{LI}^2
D) \frac{7}{2} \mathrm{LI}^2
231
MediumMHT CET2025
The self-inductance of a circuit is numerically equal to
Options:
A) the work done in establishing the magnetic flux associated with circuit.
B) twice the work done in establishing the magnetic flux associated with unit current in the circuit.
C) thrice the work done in establishing the magnetic flux associated with unit current in the circuit.
D) the work done in establishing the magnetic flux associated with unit current in the circuit.
232
MediumMHT CET2025
Two conducting circular loops of radii R_1 and \mathrm{R}_2 are placed in the same plane with their centres coinciding. If R_1>R_2, the mutual inductance M between them will be directly proportional to
Options:
A) \frac{\mathrm{R}_1}{\mathrm{R}_2}
B) \frac{R_2}{R_1}
C) \frac{\mathrm{R}_1^2}{\mathrm{R}_2}
D) \frac{R_2^2}{R_1}
233
MediumMHT CET2024
A circular coil of resistance ' R ', area ' A ', number of turns ' N ' is rotated about its vertical diameter with angular speed ' \omega ' in a uniform magnetic field of magnitude ' B '. The average power dissipated in a complete cycle is
Options:
A) \frac{\mathrm{N}^2 \mathrm{~A}^2 \mathrm{~B}^2 \omega^2}{2 \mathrm{R}}
B) \frac{\mathrm{BNA} \omega}{\mathrm{R}}
C) \frac{\mathrm{BNA} \omega}{2 \mathrm{R}}
D) \frac{N^2 A^2 B^2 \omega^2}{R}
234
MediumMHT CET2024
A coil is wound on a core of rectangular crosssection. If all the linear dimensions of the core are increased by a factor 2 and number of turns per unit length of coil remains same, the self inductance increases by a factor of (Assume, permeability is same)
Options:
A) 16
B) 8
C) 4
D) 2
235
MediumMHT CET2024
A graph of magnetic flux (\phi) versus current (I) is shown for 4 different inductors \mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}. Minimum value of inductance is for inductor
Options:
A) P
B) Q
C) R
D) S
236
MediumMHT CET2024
The mutual inductance of two coils is 45 mH . The self-inductance of the coils are \mathrm{L}_1=75 \mathrm{mH} and \mathrm{L}_2=48 \mathrm{mH}. The coefficient of coupling between the two coils is
Options:
A) 0.3
B) 0.4
C) 0.75
D) 1.0
237
MediumMHT CET2024
A coil of resistance 250 \Omega is placed in a magnetic field. If the magnetic flux (\phi) linked with the coil varies with time t(\mathrm{~s}) as \phi=50 \mathrm{t}^2+7. The current in the coil at t=4 \mathrm{~s} is
Options:
A) 1.3 A
B) \quad 1.4 \mathrm{~A}
C) \quad 1.5 \mathrm{~A}
D) 1.6 A
238
MediumMHT CET2024
A metal disc of radius R rotates with an angular velocity \omega about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is
Options:
A) \mathrm{B} \pi \mathrm{R}^2
B) \frac{2 \mathrm{~B} \pi^2 \mathrm{R}^2}{\omega}
C) \mathrm{B} \pi \mathrm{R}^2 \omega
D) \frac{\mathrm{BR}^2 \omega}{2}
239
MediumMHT CET2024
An air cored coil has a self inductance 0.1 H . A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced \left(\frac{1}{10}\right)^{\text {th }}. The value of self inductance is
Options:
A) 0.1 H
B) 1 mH
C) 1 H
D) 10 mH
240
MediumMHT CET2024
When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance becomes
Options:
A) (9) times
B) two times
C) three times
D) four times
241
MediumMHT CET2024
Two solenoids of equal number of turns have their lengths as well as radii in the same ratio 1: 3. The ratio of their self inductance will be
Options:
A) 1: 3
B) 1: 9
C) 9: 1
D) 3: 2
242
MediumMHT CET2024
If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will
Options:
A) remain constant
B) be halved
C) become 9 times
D) become \frac{1}{9} times
243
MediumMHT CET2024
The number of turns in the primary of a transformer are 1000 and in secondary 3000. If 80 V a.c. is applied to the primary, the potential difference per turn of the secondary coil is
Options:
A) 0.02 V
B) 0.04 V
C) 0.08 V
D) 0.16 V
244
MediumMHT CET2024
A closely wound coil of 100 turns and of crosssection 1 \mathrm{~cm}^2 has coefficient of self inductance 1 mH . The magnetic induction at the centre of the core of a coil when a current of 2 A flows in it, will be (in \mathrm{Wb} / \mathrm{m}^2 )
Options:
A) 0.2
B) 0.4
C) 0.8
D) 1
245
MediumMHT CET2024
When the number of turns in a coil is doubled without any change in the length of the coil, its self-inductance
Options:
A) becomes 4 times.
B) becomes 2 times.
C) gets halved.
D) remains unchanged.
246
MediumMHT CET2024
The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV Current in the primary is reduced from 6 A to 3 A . The time required for the change of current is
Options:
A) 3 \times 10^{-3} \mathrm{~s}
B) 3 \times 10^{-2} \mathrm{~s}
C) 6 \times 10^{-3} \mathrm{~s}
D) 3 \times 10^{-2} \mathrm{~s}
247
MediumMHT CET2024
If current of 4 A produces magnetic flux of 3 \times 10^{-3} \mathrm{~Wb} through a coil of 400 turns, the energy stored in the coil will be
Options:
A) 1.2 J
B) 2.4 J
C) 24 J
D) 240 J
248
MediumMHT CET2024
Two concentric circular coils having radii ' r_1{ }^{\prime} and ' r_2 ' \left(r_2 \ll r_1\right) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ( \mu_0= permeability of free space) (Both coils have single turn)
Options:
A) \frac{\mu_0 \pi r_2}{2 r_1}
B) \frac{\mu_0 \pi}{2 r_1 r_2}
C) \frac{\mu_0 \pi r_1}{2 r_2}
D) \frac{\mu_0 \pi r_2^2}{2 r_1}
249
MediumMHT CET2024
An inductor coil of inductance L is divided into two parts and both parts are connected in parallel. The net inductance is
Options:
A) L
B) 2L
C) \frac{\mathrm{L}}{2}
D) \frac{\mathrm{L}}{4}
250
MediumMHT CET2024
Two coils have a mutual inductance 0.003 H . The current changes in the first coil according to equation I=I_0 \sin \omega t, where I_0=8 \mathrm{~A} and \omega=100 \pi \mathrm{rad} \mathrm{s}^{-1}. The maximum value of e.m.f. in the second coil is
Options:
A) 2 \pi \mathrm{~V}
B) 2.4 \pi \mathrm{~V}
C) 5 \pi \mathrm{~V}
D) 7.2 \pi \mathrm{~V}
251
MediumMHT CET2024
The current in LR circuit if reduced to half What will be the energy stored in it?
Options:
A) 4 times
B) 2 times
C) half times
D) \left(\frac{1}{4}\right)^{\text {th }} times
252
MediumMHT CET2024
Two coils of self-inductance 25 mH and 9 mH are placed close together such that the effective flux in one coil is completely linked with the other The mutual inductance between these coils is
Options:
A) 34 mH
B) 16 mH
C) 15 mH
D) 6 mH
253
MediumMHT CET2024
Consider the following circuit. By keeping \mathrm{S}_1 closed, the capacitor is fully charged and then S_1 is opened and S_2 is closed, then
Options:
A) At time \mathrm{t}=0, the energy stored in the circuit is purely in the form of magnetic energy.
B) At \mathrm{t}>0, there is no exchange of energy between L and C.
C) At any time \mathrm{t}>0, the current in the circuit is in the same direction.
D) At any time \mathrm{t}>0, the instantaneous current in the circuit may be \mathrm{V} \sqrt{\frac{\mathrm{c}}{\mathrm{L}}}
254
MediumMHT CET2024
A square loop ABCD is moving with constant velocity ' \vec{v} ' in a uniform magnetic field ' \vec{B} ' which is perpendicular to the plane of paper and directed outward. The resistance of coil is ' R ', then the rate of production of heat energy in the loop is [ L - length of side of loop]
Options:
A) \frac{B^2 L^2 V}{R}
B) \frac{B^2 L^2 V^2}{R}
C) \frac{B^2 L V^2}{R}
D) \frac{\mathrm{BLV}^2}{\mathrm{R}}
255
MediumMHT CET2024
A metal rod of length ' l ' rotates about one of its ends in a plane perpendicular to a magnetic field of induction ' B '. If the e.m.f. induced between the ends of the rod is ' e ', then the number of revolutions made by the rod per second is
Options:
A) \frac{\mathrm{e}}{\mathrm{B} \pi^2 l}
B) \frac{\mathrm{e}}{\mathrm{B} \pi l^2}
C) \frac{\mathrm{B}^2}{\mathrm{e} \pi l}
D) \frac{\pi l^2}{\mathrm{eB}}
256
MediumMHT CET2024
Two coils have a mutual inductance 5 \times 10^{-3} \mathrm{H}. The current changes in the first coil according to the equation I_1=I_0 \sin \omega t where I_0=10 \mathrm{~A} and \omega=100 \pi \mathrm{rad} / \mathrm{s}. What is the value of the maximum e.m.f. in the coil?
Options:
A) 2 \pi \mathrm{~V}
B) 3 \pi \mathrm{~V}
C) 4 \pi \mathrm{~V}
D) 5 \pi \mathrm{~V}
257
MediumMHT CET2024
The magnetic flux through a coil of resistance ' R ' changes by an amount ' \Delta \phi ' in time ' \Delta t '. The amount of induced current and induced charge in the coil are respectively
Options:
A) \left(\frac{\Delta \phi}{\Delta t}\right) R and \frac{R}{\Delta \phi}
B) \frac{\Delta \phi}{\mathrm{R}} and \mathrm{R}\left(\frac{\Delta \mathrm{t}}{\Delta \phi}\right)
C) \frac{\Delta \phi}{\mathrm{R}}+\mathrm{R} and \frac{\Delta \phi}{\Delta \mathrm{t}}
D) \left(\frac{\Delta \phi}{\Delta \mathrm{t}}\right) \times \frac{1}{\mathrm{R}} and \frac{\Delta \phi}{\mathrm{R}}
258
MediumMHT CET2024
The planar concentric rings of metal wire having radii r_1 and r_2 (with r_1>r_2 ) are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( \mu_0= permeability of free space)
Options:
A) \frac{\mu_0 \pi\left(r_1+r_2\right)^2}{2 r_2}
B) \frac{\mu_0 \pi\left(r_1-r_2\right)^2}{2 r_1}
C) \frac{\mu_0 \pi r_1^2}{2 r_2}
D) \frac{\mu_0 \pi r_2^2}{2 r_1}
259
MediumMHT CET2024
A magnetic field of 2 \times 10^{-2} \mathrm{~T} acts at right angles to a coil of area 100 \mathrm{~cm}^2 with 50 turns, The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time t. The value of ' t ' is (in second)
Options:
A) 0.1 s
B) 0.01 s
C) 1 s
D) 20 s
260
MediumMHT CET2024
A current of 0.5 A is passed through winding of a long solenoid having 400 turns. The magnetic flux linked with each turn is 3 \times 10^{-3} \mathrm{~Wb}. The self inductance of the solenoid is
Options:
A) 2.4 H
B) 2.0 H
C) 1.2 H
D) 0.6 H
261
MediumMHT CET2024
A square loop of area 25 \mathrm{~cm}^2 has a resistance of 10 \Omega. The loop is placed in uniform magnetic field of magnitude 40 T . The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1 second, will be
Options:
A) 2.5 \times 10^{-3} \mathrm{~J}
B) 1.0 \times 10^{-3} \mathrm{~J}
C) 1.0 \times 10^{-4} \mathrm{~J}
D) 5 \times 10^{-3} \mathrm{~J}
262
MediumMHT CET2024
A graph of magnetic flux (\phi) versus current ( 1 ) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor
Options:
A) D
B) C
C) B
D) A
263
MediumMHT CET2024
A circular coil of resistance R, area A, number of turns ' N ' is rotated about its vertical diameter with angular speed ' \omega ' in a uniform magnetic field of magnitude ' B '. The average power dissipated in a complete cycle is
Options:
A) \frac{\mathrm{N}^2 \mathrm{~A}^2 \mathrm{~B}^2 \omega^2}{2 \mathrm{R}}
B) \frac{\mathrm{BNA} \omega}{\mathrm{R}}
C) \frac{\mathrm{N}^2 \mathrm{AB}}{2 \mathrm{R} \omega^2}
D) \frac{B A \omega}{2 N R}
264
MediumMHT CET2024
Two coils are kept near each other. When no current passess through first coil and current in the 2^{\text {nd }} coil increases at the rate 10 \mathrm{~A} / \mathrm{s}, the e.m.f. in the 1^{\mathbb{P}} coil is 20 mV . When no current passes through 2^{\text {nd }} coil and 3.6 A current passes through 1^2 coil the flux linkage in coil 2 is
Options:
A) 1.2 \times 10^{-3} \mathrm{~Wb}
B) 1.8 \times 10^{-3} \mathrm{~Wb}
C) 3.6 \times 10^{-3} \mathrm{~Wb}
D) 7.2 \times 10^{-3} \mathrm{~Wb}
265
MediumMHT CET2024
A rod of length ' l ' is rotated with angular velocity ' \omega ' about its one end, perpendicular to a magnetic field of induction ' B '. The e.m.f. induced in the rod is
Options:
A) \mathrm{B} l^2 \omega
B) 0.5 \mathrm{~B} l^2 \omega
C) B / \omega
D) 0.5 \mathrm{~B} / \omega
266
MediumMHT CET2024
In an a. c. generator, when the plane of the coil is perpendicular to the magnetic field
Options:
A) magnetic flux is zero and induced e.m.f. is maximum.
B) magnetic flux is maximum and induced e.m.f. is zero.
C) both magnetic flux and induced e.m.f. are maximum.
D) both magnetic flux and induced e.m.f. are zero.
267
MediumMHT CET2024
An air cored coil has self inductance of 0.1 H . A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced to \left(\frac{1}{10}\right)^{\text {th }}. The value of self inductance is now
Options:
A) 0.1 H
B) 1 mH
C) 1 H
D) 10 mH
268
MediumMHT CET2024
The coil and magnet are moved in the same direction with same speed (V). The induced e.m.f. is
Options:
A) zero.
B) proportional to V.
C) proportional to \mathrm{V}^{-1}.
D) finite but does not depend on V.
269
MediumMHT CET2024
The magnetic energy stored in an inductor of inductance 5 \mu \mathrm{H} carrying a current of 2 A is
Options:
A) 10 mJ
B) 5 mJ
C) 10 \mu \mathrm{~J}
D) 5 \mu \mathrm{~J}
270
MediumMHT CET2024
A bicycle wheel of radius ' R ' has ' n ' spokes. It is rotating at the rate of ' F ' r.p.m. perpendicular to the horizontal component of earth's magnetic field \vec{B}. The e.m.f. induced between the rim and the centre of the wheel is
Options:
A) \frac{1}{2} \mathrm{~B} \pi \mathrm{FR}^2
B) \mathrm{B} \pi \mathrm{FR}^2
C) \frac{1}{\mathrm{n}} \mathrm{B} \pi \mathrm{FR}
D) B \pi \mathrm{FR}^2 n
271
MediumMHT CET2023
A long solenoid has 1500 turns. When a current of $3.5 \mathrm{~A} flows through it, the magnetic flux linked with each turn of solenoid is 2.8 \times 10^{-3}$ weber. The self-inductance of solenoid is
Options:
A) 1.2 H
B) 2.4 H
C) 3.6 H
D) 6 H
272
MediumMHT CET2023
A coil having effective area A, is held with its plane normal to magnetic field of induction B. The magnetic induction is quickly reduced by $25 \%$ of its initial value in 2 second. Then the e.m.f. induced across the coil will be
Options:
A) \frac{\mathrm{AB}}{8}
B) \frac{\mathrm{AB}}{2}
C) \frac{3 \mathrm{AB}}{4}
D) \frac{3 \mathrm{AB}}{8}
273
MediumMHT CET2023
The self induction (L) produced by solenoid of length '$l' having '\mathrm{N}' number of turns and cross sectional area 'A' is given by the formula (\phi= magnetic flux, \mu_0=$ permeability of vacuum)
Options:
A) \mathrm{L}=\mathrm{N} \phi
B) \mathrm{L}=\mu_0 \mathrm{NAl}
C) \mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{l}
D) \mathrm{L}=\frac{\mu_0 \mathrm{NA}}{l}
274
MediumMHT CET2023
A magnetic field of $2 \times 10^{-2} \mathrm{~T} acts at right angles to a coil of area 100 \mathrm{~cm}^2 with 50 turns. The average e.m.f. induced in the coil is 0.1 \mathrm{~V}, when it is removed from the field in time 't'. The value of 't$' is
Options:
A) 2 \times 10^{-3} \mathrm{~s}
B) 0.5 \mathrm{~s}
C) 0.1 \mathrm{~s}
D) 1 \mathrm{~s}
275
MediumMHT CET2023
The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to
Options:
A) varying electric field
B) varying magnetic field
C) the iron core
D) heat produced in the coil
276
MediumMHT CET2023
A metal disc of radius $R rotates with an angular velocity \omega about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B$ acting perpendicular to the plane of the disc. The magnitude of induced emf between the rim and axis of the disc is
Options:
A) \pi B R^2
B) \frac{2 \pi^2 B R^2}{\omega}
C) \pi B R^2 \omega
D) \frac{B R^2 \omega}{2}
277
MediumMHT CET2023
A conductor $10 \mathrm{~cm} long is moves with a speed 1 \mathrm{~m} / \mathrm{s} perpendicular to a field of strength 1000 \mathrm{~A} / \mathrm{m}. The emf induced in the conductor is (Given : \mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}$ )
Options:
A) \pi \mathrm{~mV}
B) 2 \pi \mathrm{~mV}
C) 40 \pi \mu \mathrm{~V}
D) 4 \pi \mu \mathrm{~V}
278
MediumMHT CET2023
Three coils of inductance $\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H} and \mathrm{L}_3=6 \mathrm{H}$ are connected such that they are separated from each other. To obtain the effective inductance of 1 henry, out of the following combinations as shown in figure, the correct one is
Options:
A) S
B) P
C) R
D) Q
279
MediumMHT CET2023
The magnet is moved towards the coil with speed '$\mathrm{V}'. The induced e.m.f. in the coil is '\mathrm{e}'. The magnet and the coil move away from one another each moving with speed '\mathrm{V}$'. The induced e.m.f. in the coil is
Options:
A) \mathrm{e}
B) 2 \mathrm{e}
C) \frac{\mathrm{e}}{2}
D) 4 \mathrm{e}
280
MediumMHT CET2023
A transformer has 20 turns in the primary and 100 turns in the secondary coil. An ac voltage of $\mathrm{V}_{\text {in }}=600 \sin 314 \mathrm{t}$ is applied to primary terminal of transformer. Then maximum value of secondary output voltage obtained in volt is
Options:
A) 600
B) 300
C) 3000
D) 6000
281
MediumMHT CET2023
SI units of self inductance is
Options:
A) \frac{\mathrm{V}-\mathrm{A}}{\mathrm{S}}
B) \frac{\mathrm{V}}{\mathrm{A}-\mathrm{S}}
C) \frac{\mathrm{V}-\mathrm{S}}{\mathrm{A}}
D) \frac{\mathrm{A}}{\mathrm{V}-\mathrm{S}}
282
MediumMHT CET2023
An air craft of wing span $40 \mathrm{~m} files horizontally in earth's magnetic field 5 \times 10^{-5} \mathrm{~T} at a speed of 500 \mathrm{~m} / \mathrm{s}$. The e.m.f. generated between the tips of the wings of the air craft is
Options:
A) 0.5 V
B) 1 V
C) 1.2 V
D) 1.5 V
283
MediumMHT CET2023
Inductance per unit length near the middle of a long solenoid is $\left(\mu_0=\right. permeability of free space, \mathrm{n}= number of turns per unit length, \mathrm{d}=$ the diameter of the solenoid)
Options:
A) \mu_0 \pi\left(\frac{\mathrm{nd}}{2}\right)^2
B) 4 \mu_0 \pi\left(\frac{\mathrm{nd}}{2}\right)
C) \left(\frac{\mu_0 \pi n d}{2}\right)
D) \frac{4 \mu_0 \pi}{\mathrm{n}^2 \mathrm{~d}^2}
284
MediumMHT CET2023
Two inductors of $60 \mathrm{~mH} each are joined in parallel. The current passing through this combination is 2.2 \mathrm{~A}$. The energy stored in this combination of inductors in joule is
Options:
A) 0.0333
B) 0.0667
C) 0.0726
D) 0.0984
285
MediumMHT CET2023
Two coils have a mutual inductance of $0.004 \mathrm{~H}. The current changes in the first coil according to equation \mathrm{I}=\mathrm{I}_0 \sin \omega \mathrm{t}, where \mathrm{I}_0=10 \mathrm{~A} and \omega=50 ~\pi \mathrm{~rad} ~\mathrm{s}^{-1}$. The maximum value of e.m.f. in the second coil in volt is
Options:
A) 5 \pi
B) 4 \pi
C) 2.5 \pi
D) 2 \pi
286
MediumMHT CET2023
The magnetic flux through a circuit of resistance '$R' changes by an amount \Delta \phi in the time \Delta t. The total quantity of electric charge 'Q$' which passes during this time through any point of the circuit is
Options:
A) -\frac{\Delta \phi}{\Delta t}+R
B) \frac{\Delta \phi}{\mathrm{R}}
C) \frac{\Delta \phi}{\Delta t}
D) \frac{\Delta \phi}{\Delta t} \times R
287
MediumMHT CET2023
The self inductance '$L' of a solenoid of length 'l' and area of cross-section '\mathrm{A}', with a fixed number of turns '\mathrm{N}$' increases as
Options:
A) both $l and A$ increase
B) l decreases and \mathrm{A}$ increases
C) l$ increases and A decreases
D) both $l$ and A decrease
288
MediumMHT CET2023
A coil having effective area '$A' is held with its plane normal to a magnitude field of induction '\mathrm{B}'. The magnetic induction is quickly reduced to 25 \%$ of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be
Options:
A) \frac{\mathrm{BA}}{4}
B) \frac{\mathrm{BA}}{2}
C) \frac{3 \mathrm{BA}}{8}
D) \frac{3 \mathrm{BA}}{4}
289
MediumMHT CET2023
A coil of radius '$r' is placed on another coil (whose radius is \mathrm{R} and current flowing through it is changing) so that their centres coincide (\mathrm{R} \gg \mathrm{r}). If both the coils are coplanar then the mutual inductance between them is ( \mu_0=$ permeability of free space)
Options:
A) \frac{\mu_0 \pi \mathrm{R}^2}{2 \mathrm{r}}
B) \frac{\mu_0 \pi r^2}{2 R}
C) \frac{\mu_0 \pi r^2}{R}
D) \mu_0 \pi R^2
290
MediumMHT CET2023
When a current of $1 \mathrm{~A} is passed through a coil of 100 turns, the flux associated with it is 2.5 \times 10^{-5} \mathrm{~Wb} /$ turn. The self inductance of the coil in millihenry is
Options:
A) 40
B) 25
C) 4
D) 2.5
291
MediumMHT CET2023
The mutual inductance of a pair of coils, each of '$N' turns, is 'M' henry. If a current of 'I' ampere in one of the coils is brought to zero in 't$' second, the e. m. f. induced per turn in the other coil in volt is
Options:
A) \frac{\mathrm{MI}}{\mathrm{t}}
B) \frac{\mathrm{NMI}}{\mathrm{t}}
C) \frac{\mathrm{NM}}{\mathrm{It}}
D) \frac{\mathrm{MI}}{\mathrm{Nt}}
292
MediumMHT CET2023
To manufacture a solenoid of length $1 \mathrm{~m} and inductance 1 \mathrm{~mH}$, the length of thin wire required is (cross - sectional diameter of a solenoid is considerably less than the length)
Options:
A) 0.10 m
B) 0.10 km
C) 1 km
D) 10 km
293
MediumMHT CET2023
A hollow metal pipe is held vertically and bar magnet is dropped through it with its length along the axis of the pipe. The acceleration of the falling magnet is ( $\mathrm{g}=$ acceleration due to gravity)
Options:
A) equal to g.
B) less than $\mathrm{g}$.
C) more than g.
D) zero.
294
MediumMHT CET2023
Two concentric circular coils having radii $r_1 and r_2\left(r_2 << r_1\right) are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, \mu_0=$ permeability of free space)
Options:
A) \frac{\mu_0 \pi r_2^2}{2 r_1}
B) \frac{\mu_0 \pi r_2}{2 r_1}
C) \frac{\mu_0 \pi r_2^2}{r_1^2}
D) \frac{\mu_0 \pi r_2}{r_1}
295
MediumMHT CET2023
A graph of magnetic flux $(\phi)$ versus current (I) is plotted for four inductors A, B, C, D. Larger value of self inductance is for inductor
Options:
A) A
B) B
C) C
D) D
296
MediumMHT CET2023
A square loop of area $25 \mathrm{~cm}^2 has a resistance of 10 \Omega. This loop is placed in a uniform magnetic field of magnitude 40 \mathrm{~T}$. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in one second, will be
Options:
A) 1 \times 10^{-4} \mathrm{~J}
B) 1.0 \times 10^{-3} \mathrm{~J}
C) 5 \times 10^{-3} \mathrm{~J}
D) 2.5 \times 10^{-3} \mathrm{~J}
297
MediumMHT CET2023
Two conducting circular loops of radii '$R_1' and 'R_2' are placed in the same plane with their centres coinciding. If R_1>R_2, the mutual inductance M$ between them will be directly proportional to
Options:
A) \frac{R_1}{R_2}
B) \frac{R_2}{R_1}
C) \frac{R_1^2}{R_2}
D) \frac{R_2^2}{R_1}
298
MediumMHT CET2023
If current '$I' is flowing in the closed circuit with collective resistance 'R', the rate of production of heat energy in the loop as we pull it along with a constant speed '\mathrm{V}' is ( \mathrm{L}= length of conductor, \mathrm{B}=$ magnetic field)
Options:
A) \frac{\mathrm{BLV}}{\mathrm{R}}
B) \frac{\mathrm{B}^2 \mathrm{~L}^2 \mathrm{~V}^2}{\mathrm{R}^2}
C) \frac{B L V}{R^2}
D) \frac{\mathrm{B}^2 \mathrm{~L}^2 \mathrm{~V}^2}{\mathrm{R}}
299
MediumMHT CET2023
Two coils $\mathrm{A} and \mathrm{B} have mutual inductance 0.008 \mathrm{H}. The current changes in the coil A, according to the equation \mathrm{I}=\mathrm{I}_{\mathrm{m}} \sin \omega \mathrm{t}, where \mathrm{I}_{\mathrm{m}}=5 \mathrm{~A} and \omega=200 \pi ~\mathrm{rad} ~\mathrm{s}^{-1}. The maximum value of the e.m.f. induced in the coil B$ in volt is
Options:
A) 4 \pi
B) 8 \pi
C) 10 \pi
D) 16 \pi
300
MediumMHT CET2023
The mutual inductance (M) of the two coils is $3 ~\mathrm{H}. The self inductances of the coils are 4 ~\mathrm{H} and 9 ~\mathrm{H}$ respectively. The coefficient of coupling between the coils is
Options:
A) 0.3
B) 0.4
C) 0.5
D) 0.6
301
MediumMHT CET2023
The magnetic flux through a loop of resistance $10 ~\Omega varying according to the relation \phi=6 \mathrm{t}^2+7 \mathrm{t}+1, where \phi is in milliweber, time is in second at time \mathrm{t}=1 \mathrm{~s}$ the induced e.m.f. is
Options:
A) 12 \mathrm{~mV}
B) 7 \mathrm{~mV}
C) 19 \mathrm{~mV}
D) 19 \mathrm{~V}
302
MediumMHT CET2023
An electron (mass $\mathrm{m} ) is accelerated through a potential difference of 'V' and then it enters in a magnetic field of induction 'B' normal to the lines. The radius of the circular path is (\mathrm{e}=$ electronic charge)
Options:
A) \sqrt{\frac{2 \mathrm{eV}}{\mathrm{m}}}
B) \sqrt{\frac{2 \mathrm{Vm}}{\mathrm{eB}^2}}
C) \sqrt{\frac{2 V m}{e B}}
D) \sqrt{\frac{2 V m}{\mathrm{e}^2 \mathrm{~B}}}
303
MediumMHT CET2023
A conducting wire of length $2500 \mathrm{~m} is kept in east-west direction, at a height of 10 \mathrm{~m} from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire =25 \sqrt{2} \Omega, acceleration due to gravity \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{~B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}$ )
Options:
A) 0.2 \mathrm{~A}
B) 0.02 \mathrm{~A}
C) 0.01 \mathrm{~A}
D) 2 \mathrm{~A}
304
MediumMHT CET2023
Self inductance of solenoid is
Options:
A) directly proportional to current flowing through the coil.
B) directly proportional to the length.
C) directly proportional to its area of cross-section.
D) inversely proportional to the area of cross-section.
305
MediumMHT CET2022
The magnetic flux through a coil of resistance '$R' changes by an amount '\Delta \phi' in time '\Delta \mathrm{t}'. The total quantity of induced electric charge '\mathrm{Q}$' is
Options:
A) -\frac{\Delta \phi}{\Delta \mathrm{t}}+\mathrm{R}
B) \frac{\Delta \phi}{\Delta \mathrm{t}} \times \mathrm{R}
C) \frac{\Delta \phi}{\mathrm{R}}
D) \frac{\Delta \phi}{\Delta t}
306
MediumMHT CET2022
Self inductance of a solenoid cannot be increased by
Options:
A) decreasing its length
B) increasing its area of cross-section
C) increasing the current through it
D) increasing the number of turns in it
307
MediumMHT CET2022
A graph of magnetic flux $(\phi)$ versus current (I) is drawn for four inductors A, B, C, D. Larger value of self inductance is for inductor.
Options:
A) D
B) B
C) C
D) A
308
MediumMHT CET2021
A current 'I' produces a magnetic flux '$\phi' per turn in a coil of 'n' turns. Self inductance of the coil is 'L$'. The relation between them is
Options:
A) \mathrm{nLI}=\phi
B) \frac{\mathrm{nL}}{\mathrm{I}}=\phi
C) \frac{\mathrm{LI}}{\mathrm{n}^2}=\phi
D) \frac{\mathrm{LI}}{\mathrm{n}}=\phi
309
MediumMHT CET2021
A current $I=10 \sin (100 \pi t) ampere, is passed in a coil which induces a maximum emf 5 \pi$ volt in neighbouring coil. The mutual inductance of two coils is
Options:
A) 5 \mathrm{~mH}
B) 10 \mathrm{~mH}
C) 15 \mathrm{~mH}
D) 25 \mathrm{~mH}
310
MediumMHT CET2021
A rectangular loop $\mathrm{PQMN} with movable arm \mathrm{PQ} of length 12 \mathrm{~cm} and resistance 2 \Omega is placed in a uniform magnetic field of 0.1 \mathrm{~T} acting perpendicular to the plane of the loop as shown in figure. The resistances of the arms MN, NP and MQ are negligible. The current induced in the loop when arm PQ is moved with velocity 20 \mathrm{~ms}^{-1}$ is
Options:
A) 0.12 A
B) 0.06 A
C) 0.24 A
D) 0.18 A
311
MediumMHT CET2021
A coil has an area $0.06 \mathrm{~m}^2 and it has 600 turns. After placing the coil in a magnetic field of strength 5 \times 10^{-5} \mathrm{Wbm}^{-2}, it is rotated through 90^{\circ} in 0.2 second. The magnitude of average e.m.f induced in the coil is \left[\cos 0^{\circ}=\sin 90^{\circ}=1 \text { and } \sin 0^{\circ}=\cos 90^{\circ}=0\right]
Options:
A) 12 \times 10^{-3} \mathrm{~V}
B) 3 \mathrm{~mV}
C) 3 \mathrm{~V}
D) 9 \times 10^{-3} \mathrm{~V}
312
MediumMHT CET2021
. If the current of '$I' A gives rise to a magnetic flux '\phi' through a coil having 'N$' turns then mangetic energy stored in the medium surrounding the coil is
Options:
A) \frac{\mathrm{N} \phi \mathrm{I}}{4}
B) \frac{\mathrm{N} \phi \mathrm{I}}{2}
C) \frac{\mathrm{NI}}{2 \phi}
D) \frac{\mathrm{N} \phi}{2 \mathrm{I}}
313
MediumMHT CET2021
A conducting loop of resistance 'R' is moved to magnetic field, the total induced charge depends upon
Options:
A) initial magnetic flux and R.
B) final magnetic flux and R.
C) the total change in magnetic flux and R.
D) the rate of change of magnetic flux and $\mathrm{R}$.
314
MediumMHT CET2021
The self inductance of solenoid of length $31.4 \mathrm{~cm}, area of cross section 10^{-3} \mathrm{~m}^2 having total number of turns 500 will be nearly [\mu_0=4 \pi \times 10^{-7}$ SI unit]
Options:
A) 3 \times 10^{-6} \mathrm{H}
B) 2 \times 10^{-6} \mathrm{H}
C) 0.5 \times 10^{-6} \mathrm{H}
D) 4 \times 10^{-6} \mathrm{H}
315
MediumMHT CET2021
A circuit has self-inductance 'L' H and carries a current 'I' A. To prevent sparking when the circuit is switched off, a capacitor which can withstand 'V' volt is used. The least capacitance of the capacitor connected across the switch must be equal to
Options:
A) \frac{\mathrm{IV}}{\mathrm{L}}
B) \mathrm{L}\left(\frac{\mathrm{V}}{\mathrm{L}}\right)^2
C) \mathrm{L}\left(\frac{\mathrm{I}}{\mathrm{V}}\right)^2
D) \frac{\mathrm{LI}}{\mathrm{V}}
316
MediumMHT CET2021
Eddy currents are produced when
Options:
A) a thick metal plate is kept in a steady magnetic field
B) a circular coil is placed in a steady magnetic field
C) a steady current is passed through a coil
D) a thick metal plate is kept in a varying magnetic field
317
MediumMHT CET2021
The magnitude of flux linked with coil varies with time as $\phi=3 t^2+4 t+7. The magnitude of induced e.m.f. at t=2 \mathrm{~s}$ is
Options:
A) 3 V
B) 16 V
C) 10 V
D) 7 V
318
MediumMHT CET2021
At what rate a single conductor should cut the magnetic flux so that current of $1.5 \mathrm{~mA} flows through it when a resistance of 5 \Omega$ is connected across its ends?
Options:
A) 6 \times 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}
B) 8 \times 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}
C) 4 \times 10^{-4} \frac{\mathrm{wb}}{\mathrm{s}}
D) 7.5 \times 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}
319
MediumMHT CET2021
the magnetic flux (in weber) in a closed circuit of resistance $20 \Omega varies with time t second according to equation \phi=5 t^2-6 t+9. The magnitude of induced current at t=0.2$ second is
Options:
A) 0.8 A
B) 1 A
C) 0.2 A
D) 0.4 A
320
MediumMHT CET2021
A circular coil of radius '$R' has 'N' turns of a wire. The coefficient of self induction of the coil will be ( \mu_0=$ permeability of free space)
Options:
A) \frac{\mu_0 N \pi R^2}{2}
B) \frac{\mu_0 N \pi R}{4}
C) \frac{\mu_0 N^2 \pi R}{2}
D) \frac{\mu_0 N \pi R}{2}
321
MediumMHT CET2021
A wire of length 1 m is moving at a speed of 2 m/s perpendicular homogenous magnetic field of 0.5 T. The ends of the wire are joined to resistance 6$\Omega$. The rate at which work is being done to keep the wire moving at that speed is
Options:
A) \frac{1}{3}$ W
B) \frac{1}{6}$ W
C) \frac{1}{12}$ W
D) 1 W
322
MediumMHT CET2021
The magnetic potential energy stored in a certain inductor is $25 \mathrm{~mJ}, when the current in the inductor is 50 \mathrm{~mA}$. This inductor is of inductance
Options:
A) 2.00 H
B) 0.20 H
C) 200 H
D) 20 H
323
MediumMHT CET2021
A wire of length '$L'; having resistance 'R' falls from a height '\ell' in earth's horizontal magnetic field 'B'. The current through the wire is ( \mathrm{g}=$ acceleration due to gravity)
Options:
A) \frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{\mathrm{R}}
B) \frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{\mathrm{R}^2}
C) \frac{2 \mathrm{BLg} \ell}{\mathrm{R}^2}
D) \frac{\mathrm{B}^2 \mathrm{~L}^2}{\mathrm{R}}
324
MediumMHT CET2021
A coil of radius '$\mathrm{r}' is placed on another coil (whose radius is '\mathrm{R}' and current through it is changing) so that their centres coincide. ( R > r$ ). If both coplanar, then the mutual inductance between them is proportional to
Options:
A) \frac{R}{r^2}
B) \frac{r}{R}
C) \frac{R}{r}
D) \frac{r^2}{R}
325
MediumMHT CET2021
A metal wire of length $2500 \mathrm{~m} is kept in east-west direction, at a height of 10 \mathrm{~m} from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire =25 \sqrt{2} \Omega, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 and Earth's horizontal component of magnetic field \left.\mathrm{B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}\right)
Options:
A) 0.2 A
B) 0.02 A
C) 0.01 A
D) 2 A
326
MediumMHT CET2021
Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop is
Options:
A) clockwise
B) anticlockwise
C) in a direction which depends on the ratio of the loop radii.
D) zero
327
MediumMHT CET2021
A straight conductor of length 0.6 M is moved with a speed of 10 ms$^{-1} perpendicular to magnetic field of induction 1.2 weber m^{-2}$. The induced e.m.f. across the conductor is
Options:
A) 6 V
B) 7.2 V
C) 0.72 V
D) 12 V
328
MediumMHT CET2020
Metal rings P and Q are lying in the same plane, where current I is increasing steadily. The induced current in metal rings is shown correctly in figure
Options:
A)
B)
C)
D)
329
MediumMHT CET2020
The length of solenoid is $I whose windings are made of material of density D and resistivity \rho. The winding resistance is R. The inductance of solenoid is [m= mass of winding wire, \mu_0=$ permeability of free space]
Options:
A) \frac{\mu_0}{4 \pi I}\left(\frac{R m}{\rho D}\right)
B) \frac{\mu_0}{2 \pi I}\left(\frac{R m}{\rho D}\right)
C) \frac{\mu_0}{2 \pi I}\left(\frac{\rho D}{R m}\right)
D) \frac{\mu_0}{4 \pi /}\left(\frac{\rho D}{R m}\right)
330
MediumMHT CET2020
A coil of $n turns and resistance R \Omega is connected in series with a resistance \frac{R}{2}. The combination is moved for time t second through magnetic flux \phi_1 to \phi_2$. The induced current in the circuit is
Options:
A) \frac{n\left(\phi_1-\phi_2\right)}{3 R t}
B) \frac{2 n\left(\phi_1-\phi_2\right)}{3 R t}
C) \frac{2 n\left(\phi_1-\phi_2\right)}{R t}
D) \frac{n\left(\phi_1-\phi_2\right)}{R t}
331
MediumMHT CET2019
2. Two coils have a mutual inductance of 0.01 H . The current in the first coil changes according to equation, I=5 \sin 200 \pi t. The maximum value of emf induced in the second coil is
Options:
A) 10 \pi V
B) 0.1 \pi \mathrm{~V}
C) \pi V
D) 0.01 \pi \mathrm{~V}
332
MediumNEET2025
A B is a part of an electrical circuit (see figure). The potential difference " V_A-V_B ", at the instant when current i=2 \mathrm{~A} and is increasing at a rate of 1 \mathrm{amp} / second is:
Options:
A) 9 volt
B) 10 volt
C) 5 volt
D) 6 volt
333
MediumNEET2024
Let us consider two solenoids $A and B, made from same magnetic material of relative permeability \mu_r and equal area of cross-section. Length of A is twice that of B and the number of turns per unit length in A is half that of B. The ratio of self inductances of the two solenoids, L_A: L_B$ is
Options:
A) 1: 2
B) 2: 1
C) 8: 1
D) 1: 8
334
MediumNEET2023
An emf is generated by an ac generator having 100 turn coil, of loop area $1 \mathrm{~m}^2. The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of 0.05 \mathrm{~T}$ perpendicular to the axis of rotation of the coil. The maximum value of emf is :-
Options:
A) 3.14 V
B) 31.4 V
C) 62.8 V
D) 6.28 V
335
MediumNEET2023
The net magnetic flux through any closed surface is :
Options:
A) Positive
B) Infinity
C) Negative
D) Zero
336
MediumNEET2022
The magnetic flux linked to a circular coil of radius R is $\phi = 2{t^3} + 4{t^2} + 2t + 5$ Wb The magnitude of induced emf in the coil at t = 5 s is
Options:
A) 192 V
B) 108 V
C) 197 V
D) 150 V
337
MediumNEET2022
A square loop of side 1 m and resistance 1 $\Omega$ is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is
Options:
A) 2 weber
B) 0.5 weber
C) 1 weber
D) Zero weber
338
MediumNEET2021
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to :
Options:
A) {{R_2^2} \over {{R_1}}}
B) {{{R_1}} \over {{R_2}}}
C) {{{R_2}} \over {{R_1}}}
D) {{R_1^2} \over {{R_2}}}
339
MediumNEET2019
A 800 turn coil of effective area 0.05 m2 is kept. perpendicular to a magnetic filed 5 × 10–5 T. When the plane of the coil is rotated by 90o around any of its coplanar axis in 0.1 s, the emf induced in the coil will be :
Options:
A) 0.2 V
B) 0.02 V
C) 2 V
D) 2 $ \times $ 10-3 V
340
MediumNEET2019
In which of the following devices, the eddy current effect is not used?
Options:
A) magnetic braking in train
B) electromagnet
C) electric heater
D) induction furnace
341
MediumNEET2017
A long solenoid of diameter 0.1 m has 2 $ \times 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 \pi 2 \Omega $, the total charge flowing through the coil during this time is
Options:
A) 16 $\mu $C
B) 32 $\mu $C
C) 16$\pi \mu $C
D) 32$\pi \mu $C
342
MediumNEET2016
A uniform magnetic field is restricted within a region of rafius r. The magnetic field changes with time at a rate ${{d\overrightarrow B } \over {dt}}$. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e.m.f. generated is
Options:
A) zero in loop 1 and zero in loop 2
B) - {{d\overrightarrow B } \over {dt}}\pi {r^2} in loop 1 and - {{d\overrightarrow B } \over {dt}}\pi {r^2}$ in loop 2
C) - {{d\overrightarrow B } \over {dt}}\pi {R^2}$ in loop 1 and zero in loop 2
D) - {{d\overrightarrow B } \over {dt}}\pi {r^2}$ in loop 1 and zero in loop 2
343
MediumNEET2016
A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4 $ \times \,{10^{ - 3}}$ Wb. The self-inductance of the solenoid is
Options:
A) 2 H
B) 1 H
C) 4 H
D) 3 H
344
MediumNEET2015
An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil ?
Options:
A) The current will reverse its direction as the electron goes past the coil
B) No current induced
C) abcd
D) adcb
345
MediumNEET2014
A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. The potential difference developed across the ring when its speed is $v$, is
Options:
A) zero
B) {{Bv\pi {r^2}} \over 2}$ and P is at higher potential
C) \pi rBV$ and R is at higher potential
D) 2rBV and R is at higher potential
346
MediumNEET2013
A current of 2.5 A flows through a coil of inductance 5 H. The magnetic flux linked with the coil is
Options:
A) 0.5 Wb
B) 12.5 Wb
C) zero
D) 2 Wb
347
MediumNEET2013
A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is
Options:
A) four times per revoluation
B) six times per revolution
C) once per revolution
D) twice per revolution
348
MediumNEET2012
In a coil of resistance 10 $\Omega $, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is
Options:
A) 8
B) 2
C) 6
D) 4
349
MediumNEET2012
A coil of resistance 400 $\Omega is placed in a magnetic field. If the magnetic flux \phi (Wb) linked with the coil varies with time t (sec) as \phi = 50{t^2} + 4$. The current in the coil at t = 2 sec is
Options:
A) 0.5 A
B) 0.1 A
C) 2 A
D) 1 A
350
MediumNEET2011
The current $i$ in a coil varies with time as shown in the figure. The variation of induced emf with time would be
Options:
A)
B)
C)
D)
351
MediumNEET2010
A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s$-$1. The induced emf when the radius is 2 cm, is
Options:
A) 2\pi \mu V
B) \pi \mu V
C) {\pi \over 2}\mu V
D) 2$\mu V
352
MediumNEET2009
A rectangular, a square, a circular and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity. $\overrightarrow V = v\widehat i$. The magnetic field is directed along the negative z axis direction. The induced emf, during the passes of these loops, out of the field region, will not remain constant for
Options:
A) The circular and the elliptical loops
B) only the ellliptical loop
C) any of the four loops
D) the rectangular, circular and elliptical loops
353
MediumNEET2009
A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is
Options:
A) 4.8$\pi \mu $V
B) 0.8$\pi \mu $V
C) 1.6$\pi \mu $V
D) 3.2$\pi \mu $V
354
MediumNEET2008
A circular disc of radius 0.2 meter is placed in a uniform magnetic field of induction ${1 \over \pi }\left( {{{Wb} \over {{m^2}}}} \right) in such a way that its axis makes an angle of 60o with \overrightarrow B .$ The magnetic flux linked with the disc is
Options:
A) 0.08 Wb
B) 0.01 Wb
C) 0.02 Wb
D) 0.06 Wb
355
MediumNEET2008
A long solenoid has 500 turns. When a current of 2 ampere is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 $ \times 10-$3 Wb. The self-inductance of the solenoid is
Options:
A) 1.0 henry
B) 4.0 henry
C) 2.5 henry
D) 2.0 henry
356
MediumNEET2006
Two coils of self inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is
Options:
A) 16 mH
B) 10 mH
C) 6 mH
D) 4 mH
357
MediumNEET2005
As a result of change in the magnetic flux linked to the closed loop as shown in the figure, an e.m.f. $V$ volt is induced in the loop. The work done (joule) in taking a charge Q coulomb once along the loop is
Options:
A) QV
B) 2QV
C) QV/2
D) zero
358
MediumNEET2004
The magnetic flux through a circuit of resistance R changes by an amount $\Delta \phi in a time \Delta t. Then the total quantity of electric charge Q that passes any point in the circuit during the time \Delta $t is represented by
Options:
A) Q = {1 \over R}.{{\Delta \phi } \over {\Delta t}}
B) Q = {{\Delta \phi } \over R}
C) Q = {{\Delta \phi } \over {\Delta t}}
D) Q = R.{{\Delta \phi } \over {\Delta t}}
359
MediumNEET2001
For a coil having L = 2 mH, current flow through it is $I = {t^2}{e^{ - t}}$ then, the time at which emf become zero
Options:
A) 2 sec
B) 1 sec
C) 4 sec
D) 3 sec
360
MediumVITEEE2023
A coil 10 turns and a resistance of $40 \Omega is connected in series with B.G. of resistance 30 \Omega. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction 10^{-2} \mathrm{~T}. If it is now turned through an angle of 60^{\circ} about on axis in its plane. Find the charge indicted in the coil. (Area of a coil =10^{-2} \mathrm{~m}^2$ )
Options:
A) 2 \times 10^{-5} \mathrm{C}
B) 3.2 \times 10^{-5} \mathrm{C}
C) 0.714 \times 10^{-5} \mathrm{C}
D) 55 \times 10^{-5} \mathrm{C}
361
MediumVITEEE2022
A disc of $10.0 \mathrm{~cm} diameter is rotated at speed of 3600 \mathrm{~rpm} inside a long solenoid of 1200 turns per metre on the axis of the solenoid and perpendicular to the plane of the disc. When a current of 1.5 \mathrm{~A}$ is passed through the solenoid, the difference in the potential between axes and circumference of the disc is nearly
Options:
A) 0.108 mV
B) 1.08 mV
C) 0.108 $\mu$V
D) 1.08 $\mu$V
362
MediumVITEEE2021
The induced emf in a coil of $10 \mathrm{H} inductance in which current varies from 9 \mathrm{~A} to 4 \mathrm{~A} in 0.2 \mathrm{~s}$ is
Options:
A) 200 V
B) 250 V
C) 300 V
D) 350 V
363
MediumVITEEE2021
A conductor of length $5 \mathrm{~cm} is moved parallel to itself with a speed of 2 \mathrm{~m} / \mathrm{s}, perpendicular to a uniform magnetic field of 10^{-3} \mathrm{~Wb} / \mathrm{m}^3$. The induced e.m.f. generated is
Options:
A) 2 \times 10^{-3} \mathrm{~V}
B) 1 \times 10^{-3} \mathrm{~V}
C) 1 \times 10^{-4} \mathrm{~V}
D) 2 \times 10^{-4} \mathrm{~V}
363
Total Questions
41
Easy
313
Medium
9
Hard
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