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 $\overrightarrow{B}$ about an axis perpendicular to $\overrightarrow{B}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when $\overrightarrow{B}$ 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 $\mathrm{B}\left(\mathrm{r}\right)={\mathrm{B}}_{\circ }{\mathrm{e}}^{-\lambda \mathrm{r}}; \lambda$ 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 $\overrightarrow{B}$ about an axis perpendicular to $\overrightarrow{B}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when $\overrightarrow{B}$ 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 $5 c{m}^2$. 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 $\overrightarrow{B}$ about an axis perpendicular to $\overrightarrow{B}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when $\overrightarrow{B}$ 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 $\overrightarrow{B}$ about an axis perpendicular to $\overrightarrow{B}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when $\overrightarrow{B}$ 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)