Electromagnetic Induction

Self-inductance of a solenoid depends on

(Shift I Memory Based)

A solenoid of radius 10 cm carrying current 0.29 A and having total 200 turns. If magnetic field inside solenoid is\( 2.9 \times 10^{-4} \mathrm{~T}\). Find length of solenoid.(Shift - II Memory Based)

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 \(\phi\) and induced emf \(\epsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

[JEE Main 2025, 29 Jan (Shift 1)]

A solenoid of radius 10 cm carrying current 0.29 A and having total 200 turns. If magnetic field inside solenoid is\( 2.9 \times 10^{-4} \mathrm{~T}\). Find length of solenoid.(Shift - II Memory Based)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R/\sqrt{{R}^{2}+{\omega }^{2}{L}^{2}}\right)\), where \(\omega\) is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below:

[JEE Main 2025, 29 Jan (Shift 1)]

A metal rod of length L rotates about one end at origin with a uniform angular velocity ω. The magnetic field radially falls off as \(\mathrm{B}(\mathrm{r})={\mathrm{B}}_{∘}{\mathrm{e}}^{-\lambda \mathrm{r}};\lambda\) being a positive constant. The induced emf (neglecting centripetal force on electrons in the rod) is:

[JEE Main 2026, 5 Apr (Shift 2)]

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B = 0.4 sin (300t) Tesla. The normal to the plane of loop makes an angle of 60° with the field. The maximum induced emf produced in the loop is ______ mV.

[JEE Main 2026, 6 Apr (Shift 2)]

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 \(\phi\) and induced emf \(\epsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

[JEE Main 2025, 29 Jan (Shift 1)]

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R/\sqrt{{R}^{2}+{\omega }^{2}{L}^{2}}\right)\), where \(\omega\) is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below:

[JEE Main 2025, 29 Jan (Shift 1)]

A disc is rotating with an angular velocity \(\omega=10 \pi \mathrm{rad} / \mathrm{s}\) in a uniform magnetic field of \(B=0.4 \mathrm{~T}\), which is directed perpendicular to the plane of the disc. The radius of the disc is 20 cm . Find the potential difference between the centre and the rim of the disc.
(Take \(\pi=3.14\) )

(Shift - II Memory Based)

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:

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:

[JEE Main 2025, 23 Jan (Shift 1)]

A disc is rotating with an angular velocity \(\omega=10 \pi \mathrm{rad} / \mathrm{s}\) in a uniform magnetic field of \(B=0.4 \mathrm{~T}\), which is directed perpendicular to the plane of the disc. The radius of the disc is 20 cm . Find the potential difference between the centre and the rim of the disc.
(Take \(\pi=3.14\) )

(Shift - II Memory Based)

A 30 cm long solenoid has 10 turns per cm and area of \(5c{m}^{2}\). The current through the solenoid coil varies from 2A to 4A in 3.14 s. The e.m.f. induced in the coil is \(\alpha \times {10}^{-5}V\). The value \(\alpha\) is ___________.

[JEE Main 2026, 8 Apr (Shift 2)]

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 \(\phi\) and induced emf \(\epsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

[JEE Main 2025, 29 Jan (Shift 1)]

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 \(\phi\) and induced emf \(\epsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

Consider \({I}_{1}\) and \({I}_{2}\) are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If \({L}_{1}=\) self inductance of coil \(1,{M}_{12}=\) mutual inductance of coil 1 with respect to coil 2 , then the value of induced emf in coil 1 will be:

[JEE Main 2025, 29 Jan (Shift 1)]

When a coil is placed in a time dependent magnetic field the power dissipated in it is P . The number of turns, area of the coil and radius of the coil wire are N, A and r respectively. For a second coils number of turns, area of the coil and radius of the coil wire are 2 N , 2A and 3 r respectively. When the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2\alpha P}\). The value of \(\alpha\) is _____

[JEE Main 2026, 2 Apr (Shift 1)]

Self-inductance of a solenoid depends on

(Shift I Memory Based)

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 T, when moves with a velocity of:

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is:

[JEE Main 2023, 8 Apr (Shift 1)]

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

[JEE Main 2023, 10 Apr (Shift 2)]

A metal disc of radius \(100\mathrm{cm}\) is rotated at a constant angular speed of \(60 \mathrm{rad} / \mathrm{s}\) in a plane at right angles to an external field of magnetic induction \(0.05 \mathrm{~Wb} / \mathrm{m}^2\). The emf induced between the centre and a point on the rim will be

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 )

[JEE Main 2023, 31 Jan (Shift 1)]

A square loop of area \(25 cm ^2\) has a resistance of \(10 \Omega\). The square loop is placed in a uniform magnetic field of magnitude \(40.0 T\). The plane of the 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

[JEE Main 2023, 29 Jan (Shift 2)]

The time taken for the magnetic energy to reach \(25 \%\) of its maximum value, when a solenoid of resistance \(R\) and inductance \(L\) is connected to a battery, is:

An inductor coil stores \(64\mathrm{J}\) of magnetic field energy and dissipates energy at the rate of \(640\mathrm{W}\) when a current of 8 A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in ..... seconds :

[JEE Main 2021, 26 Aug (Shift 1)]

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 )

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:

[JEE Main 2023, 1 Feb (Shift 2)]

A \(12\mathrm{V}\) 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:

[JEE Main 2023, 15 Apr (Shift 1)]

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason 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

[JEE Main 2023, 11 Apr (Shift 2)]

An aeroplane, with its wings spread \(10\mathrm{m}\), is flying at a speed of \(180\mathrm{km}/\mathrm{h}\) in a horizontal direction. The total intensity of earth's field at that part is \(2.5\times {10}^{-4}\mathrm{Wb}/{\mathrm{m}}^{2}\) and the angle of dip is \(60^\circ\). The emf induced between the tips of the plane wings will be

[JEE Main 2021, 26 Feb (Shift 2)]

An inductor coil stores \(64\mathrm{J}\) of magnetic field energy and dissipates energy at the rate of \(640\mathrm{W}\) when a current of 8 A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in _______ seconds.

[JEE Main 2021, 26 Aug (Shift 1)]

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:

[JEE Main 2023, 6 Apr (Shift 1)]

A conducting 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:

[JEE Main 2023, 24 Jan (Shift 1)]

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason 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 opposes the motion of the magnetic bar.
In the light of the above statements, choose the correct answer from the options given below.

[JEE Main 2023, 11 Apr (Shift 2)]

For a moving coil galvanometer, the deflection in the coil is 0.05rad when a current of is passed through it. If the torsional constant of the suspension wire is \(4.0\times {10}^{-5}\), the magnetic field is 0.01T and the number of turns in the coil is 200 , the area of each turn (in \(c{m}^{2}\) ) is:

[JEE Main 2023, 25 Jan (Shift 2)]

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}

A conducting loop of radius \(\frac{10}{\sqrt{\pi }}\mathrm{cm}\) is placed perpendicular to a uniform magnetic field of \(0.5T\). The magnetic field is decreased to zero in \(0.5\mathrm{s}\) at a steady rate. The induced \(\mathrm{emf}\) in the circular loop at \(0.25s\) is:

[JEE mains 2023]

A rod with circular cross-section area 2cm² and length 40cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is 4π × 10^–6 Wb. The relative permeability of the rod is (Given: Permeability of vacuum μ₀ = 4π × 10^–7 NA^–2)

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 T, when moves with a velocity of:

[JEE Main 2023, 8 April (Shift 2)]