Electromagnetic Induction

A coil has 100 turns, each of area \(0.05{\mathrm{m}}^{2}\) and total resistance \(1.5\Omega\). It is inserted at an instant in a magnetic field of 90 mT , with its axis parallel to the field. The charge induced in the coil at that instant is :

Consider a solenoid of length \(l\) and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field in reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms . If the emfs induced in the two time intervals are \({e}_{1}\) and \({e}_{2}\) respectively, then the value of \({e}_{1}/{\mathrm{e}}_{2}\) is

The current in a coil of 15 mH increases uniformly from zero to 4 A in 0.004 s . The emf induced in the coil will be :

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

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 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 coil has 100 turns, each of area \(0.05{\mathrm{m}}^{2}\) and total resistance \(1.5\Omega\). It is inserted at an instant in a magnetic field of 90 mT , with its axis parallel to the field. The charge induced in the coil at that instant is :

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

A circular loop A of radius \(R\) carries a current I. Another circular loop B of radius \(r\left(=\frac{R}{20}\right)\) is placed concentrically in the plane of \(A\). The magnetic flux linked with loop B is proportional to

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

A circular coil of radius 10 cm is placed in a magnetic field \(\vec{B}=(1.0\hat{i}+0.5\hat{j})\mathrm{mT}\) such that the outward unit vector normal to the surface of the coil is \((0\cdot 6\hat{i}+0\cdot 8\hat{j})\). The magnetic flux linked with the coil is :

A circular loop A of radius \(R\) carries a current I. Another circular loop B of radius \(r\left(=\frac{R}{20}\right)\) is placed concentrically in the plane of \(A\). The magnetic flux linked with loop B is proportional to

Consider a solenoid of length \(l\) and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field in reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms . If the emfs induced in the two time intervals are \({e}_{1}\) and \({e}_{2}\) respectively, then the value of \({e}_{1}/{\mathrm{e}}_{2}\) is

Two coils are placed near each other. When the current in one coil is changed at the rate of \(5\mathrm{A}/\mathrm{s}\), an emf of 2 mV is induced in the other. The mutual inductance of the two coils is

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)

Two coils are placed near each other. When the current in one coil is changed at the rate of \(5\mathrm{A}/\mathrm{s}\), an emf of 2 mV is induced in the other. The mutual inductance of the two coils is

A coil has 100 turns, each of area \(0.05{\mathrm{m}}^{2}\) and total resistance \(1.5\Omega\). It is inserted at an instant in a magnetic field of 90 mT , with its axis parallel to the field. The charge induced in the coil at that instant is :

Two coils are placed near each other. When the current in one coil is changed at the rate of \(5\mathrm{A}/\mathrm{s}\), an emf of 2 mV is induced in the other. The mutual inductance of the two coils is

The current in a coil of 15 mH increases uniformly from zero to 4 A in 0.004 s . The emf induced in the coil will be :

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is

[JEE Main 2024, 27 Jan (Shift 1)]

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

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 \(N\) turns is placed in a magnetic field \(\vec{B}\) such that \(\vec{B}\) is perpendicular to the plane of the coil. \(B\) changes with time as \(B=B_0 \cos \left(\frac{2 \pi}{T} t\right)\) where \(T\) is time period. The magnitude of emf induced in the coil will be maximum at

Here, \(n =1,2,3,4, \ldots\)

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field in reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms . If the emfs induced in the two time intervals are \({e}_{1}\) and \({e}_{2}\) respectively, then the value of \({e}_{1}/{\mathrm{e}}_{2}\) is

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field in reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms . If the emfs induced in the two time intervals are \({e}_{1}\) and \({e}_{2}\) respectively, then the value of \({e}_{1}/{\mathrm{e}}_{2}\) is

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

Consider a solenoid of length \(l\) and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :

A circular loop A of radius \(R\) carries a current I. Another circular loop B of radius \(r\left(=\frac{R}{20}\right)\) is placed concentrically in the plane of \(A\). The magnetic flux linked with loop B is proportional to

A circular coil of radius 10 cm is placed in a magnetic field \(\vec{B}=(1.0\hat{i}+0.5\hat{j})\mathrm{mT}\) such that the outward unit vector normal to the surface of the coil is \((0\cdot 6\hat{i}+0\cdot 8\hat{j})\). The magnetic flux linked with the coil is :

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:

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)]

Self-inductance of a solenoid depends on

(Shift I Memory Based)

The current in a coil of 15 mH increases uniformly from zero to 4 A in 0.004 s . The emf induced in the coil will be :

A circular coil of radius 10 cm is placed in a magnetic field \(\vec{B}=(1.0\hat{i}+0.5\hat{j})\mathrm{mT}\) such that the outward unit vector normal to the surface of the coil is \((0\cdot 6\hat{i}+0\cdot 8\hat{j})\). The magnetic flux linked with the coil is :

Assertion (A) : It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.

Reason (R) : The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.

A square shaped coil of side \(10 \mathrm{~cm}\), having 100 turns is placed perpendicular to a magnetic field which is increasing at \(1 \mathrm{~T} / \mathrm{s}\). The induced emf in the coil is

Assertion (A) : It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.
Reason (R): The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.

Two statements are given - one labelled Assertion (A) and the other labelled Reason \((R)\). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A) : The mutual inductance between two coils is maximum when the coils are wound on each other.

Reason \((R)\) : The flux linkage between two coils is maximum when they are wound on each other.

A circular coil of radius \(8.0\) cm and \(40\) turns is rotated about its vertical diameter with an angular speed of \(\frac{25}{\pi}\text{ rad s}^{-1}\) in a uniform horizontal magnetic field of magnitude \(3.0 \times 10^{-2}\) T. The maximum emf induced in the coil is:

Assertion (A) and Reason (R) type questions. Two statements are given one labelled Assertion (A) and the other labelled Reason
(R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A) : Lenz's law is a consequence of the law of conservation of energy.

Reason (R) : There is no power loss in an ideal inductor.

Assertion (A) : The mutual inductance between two coils is maximum when the coils are wound on each other.

Reason (R): The flux linkage between two coils is maximum when they are wound on each other.