Electromagnetic Induction — JEE Main PYQs

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY 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 CD of length L ($L>l$) and mass $m$ is made to sli …

Three identical coils ${\mathrm{C}}_1,{\mathrm{C}}_2$ and ${\mathrm{C}}_3$ are closely placed such that they share a common axis. ${\mathrm{C}}_2$ is exactly midway. ${\mathrm{C}}_1$ carries current $I$ in anti-clockwise direction while ${\mathrm{C}}_3$ carries curre …

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 $\left(\frac{1}{\mathrm{e}}\right)$ of its maximum value is …

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.

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 …

A capacitor C is first charged fully with potential difference of ${\mathrm{V}}_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L . In t s $25\%$ of the initial energy in the capacitor is transferred to the induct …

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ($g=10\mathrm{m}/{\mathrm{s}}^2$) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical di …

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 …

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.

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I=10\sin (\omega t)$ A, where $\omega =1000$ rad./s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed $v=1$ cm/s. The r.m.s. curr …

A conducting circular loop of area $1.0{\mathrm{m}}^2$ is placed perpendicular to a magnetic field which varies as $\mathrm{B}=\sin (100\mathrm{t})$ Tesla. If the resistance of the loop is $100\Omega$, then the average thermal energy dissipated in the loop in one period …

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 …

A circular current loop of radius R is placed inside square loop of side length $L(L\gg R)$ such that they are co-planar and their centers coincide. The permeability of free space is ${\mu }_0$. The mutual inductance between circular loop and square loop is $\_\_\_\_$.

In the given circuit below inductance values of ${\mathrm{L}}_1$, ${\mathrm{L}}_2$ and ${\mathrm{L}}_3$ are same. The magnetic energy stored in the entire circuit is $({\mathrm{U}}_{\mathrm{t}})$ and that stored in the ${\mathrm{L}}_2$ inductor is $({\mathrm{U}}_l)$. …

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

A circular loop of radius 20 cm and resistance $2\Omega$ is placed in a time varying magnetic field $\overrightarrow{\mathrm{B}}=\left(2{\mathrm{t}}^2+2\mathrm{t}+3\right)\mathrm{T}$. At $\mathrm{t}=0$, for the plane of the loop being perpendicular to the magnetic field …

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}\mathrm{J}$. The value of $\alpha$ is $\_\_\_\_$. ( …

An inductor of inductance 10 mH having resistance of $100\Omega$ is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and …

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

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

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 2N, 2A and …

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 ( $\epsilon$ ) with time ( $t$ ) is given by

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 …

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.

Consider ${\mathrm{I}}_1$ and ${\mathrm{I}}_2$ are the currents flowing simultaneously in two nearby coils $1\&2$, respectively. If $L_1=$ self inductance of coil 1 , ${\mathrm{M}}_{12}=$ mutual inductance of coil 1 with respect to coil 2 , then the value of induced emf in coil …

A coil of area A and N turns is rotating with angular velocity $\omega$ in a uniform magnetic field $\overrightarrow{\mathrm{B}}$ about an axis perpendicular to $\overrightarrow{\mathrm{B}}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when …

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 $10\pi \mathrm{rad}{\mathrm{s}}^{-1}$ about an axis through its centre and perpendicular to the disc. What is the protential difference …

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 $\mathrm{t}=0$ with a constant velocity. If the induced EMF is E $\propto {\mathrm{t}}^{\mathrm{n}}$, then value o …

A solenoid having area A and length 'l' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

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
______ …

In a coil, the current changes from -2 A to +2 A in 0.2 s and induces an emf of 0.1 V . The self inductance of the coil is :

A rod of length 60 cm rotates with a uniform angular velocity $20\mathrm{rad}{\mathrm{s}}^{-1}$ about its perpendicular bisector, in a uniform magnetic field 0.5 T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two end …

The current in an inductor is given by $I=(3t+8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ____ mH.

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:

A square loop PQRS having 10 turns, area $3.6\times 10^{-3}{\mathrm{m}}^2$ and resistance $100\Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $\mathrm{B}=0.5\mathrm{T}$ as shown. Work done in pulling the loop out of the field in 1.0 …

When a coil is connected across a 20 V dc supply, it draws a current of 5 A. When it is connected across $20\mathrm{V},50\mathrm{Hz}$ ac supply, it draws a current of 4 A. The self inductance of the coil is ____ mH.
(Take $\pi =3$)

A square loop of side 15 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 cm wide magnetic field at $t=0$. The value of induced emf in the loop at $\mathrm{t}=10\mathrm{s}$ will be :

A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $0.60\times 10^{-4}{\mathrm{Wbm}}^{-2}$. The instantaneous value of emf induced in the wire when its velocity is …

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

Two coils have mutual inductance 0.002 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 $\omega =50\pi \mathrm{rad}/\mathrm{s}$. The maximum value of emf in the …

A capacitor of capacitance $100\mu F$ is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be :

A square loop of side 10 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 s at a steady rate. Then, magnitude of induced emf i …

A coil is placed perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 T in 2 s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is:

A small square loop of wire of side $\ell$ is placed inside a large square loop of wire of side L $\left(L={\ell }^2\right)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{\mathrm{x}}\times 10^{-7}\mathrm{H}$, …

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 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 …

A rectangular loop of sides 12 cm and 5 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 …

A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and angle of dip is $30^{\circ }$. The emf induced across the blades is $N\pi \times 10^{-5}$ V. The value of N is ______.

The magnetic flux $\varphi$ (in weber) linked with a closed circuit of resistance $8\Omega$ varies with time (in seconds) as $\varphi =5t^2-36t+1$. The induced current in the circuit at $\mathrm{t}=2\mathrm{s}$ is ______ A.

An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T , when moves with a velocity of:

An oscillating LC circuit consists of a 75 mH inductor and a $1.2\mu \mathrm{F}$ capacitor. If the maximum charge to the capacitor is $2.7\mu \mathrm{C}$. The maximum current in the circuit will be $\_\_\_\_$ mA.