Electromagnetic Induction — JEE Main PYQs

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ____ $\times 10^{-8}$ H.
(Take, ${\pi }^2=10$)

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

A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A and angular frequency $700\mathrm{rad}{\mathrm{s}}^{-1}$. The central axes of the loop and solenoid coincide. The amplitu …

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 s …

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 $t=2\mathrm{s}$ to $t=4\mathrm{s}$, is ______ mV

A conducting circular loop is placed in a uniform magnetic field of 0.4 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 …

Which of the following Maxwell's equations is valid for time varying conditions but not valid for static conditions :

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $\frac{E^a}{2b}\mathrm{J}/\mathrm{s}$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ …

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 …

A 12 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 ms. The emf induced across the coil is 20 V. The inductance of the coil is :

A 20 cm long metallic rod is rotated with 210 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 T parallel to the axis exists everywhere. The emf develop …

The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside 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 unif …

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 th …

A coil has an inductance of 2 H and resistance of $4\Omega$. A 10 V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be $\_\_\_\_$ $\times 10^{-2}$ J

A metallic cube of side 15 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 T directed along z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed beca …

A conducting loop of radius $\frac{10}{\sqrt{\pi }}\mathrm{cm}$ 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:

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 :

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.

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency ${\omega }_0$. The value of x is:

A wire of length 1 m moving with velocity $8\mathrm{m}/\mathrm{s}$ at right angles to a magnetic field of 2 T . The magnitude of induced emf, between the ends of wire will be :

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 $(\mathrm{L}\gg \mathrm{R})$. The loops are coplanar and their centres coincide :

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B=0.8\mathrm{T}$. When released the radius of the loop starts shrinking at a constant rate of $2\mathrm{cm}{\mathrm{s}}^{-1}$. The induced em …

A square loop of area $25{\text{cm}}^2$ 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 i …

In an ac generator, a rectangular coil of 100 turns each having area $14\times 10^{-2}$ m² is rotated at 360 rev/min about an axis perpendicular to a uniform magnetic field of magnitude 3.0 T. The maximum value of the emf produced will be ______ V. (Take $\pi =\frac{22}{7}$)

As per the given figure, if $\frac{\mathrm{dI}}{\mathrm{dt}}=-1\mathrm{A}/\mathrm{s}$ then the value of ${\mathrm{V}}_{\mathrm{AB}}$ at this instant will be $\_\_\_\_$ V.

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 magnet …

A square shaped coil of area $70{\mathrm{cm}}^2$ having 600 turns rotates in a magnetic field of $0.4{\mathrm{wbm}}^{-2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field.
If the coil completes 500 revolution in a minute …

A capacitor of capacitance $500\mu \mathrm{F}$ is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be ______ A.

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be ____ A.

A small square loop of wire of side $l$ is placed inside a large square loop of wire $\mathrm{L}(\mathrm{L}\gg l)$. Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is :

In a coil of resistance $8\Omega$, the magnetic flux due to an external magnetic field varies with time as $\varphi =\frac{2}{3}\left(9-t^2\right)$. The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

A conducting circular loop is placed in $\mathrm{X}-\mathrm{Y}$ plane in presence of magnetic field $\overrightarrow{\mathrm{B}}=\left(3{\mathrm{t}}^3\hat{\mathrm{j}}+3{\mathrm{t}}^2\hat{\mathrm{k}}\right)$ in SI unit. If the radius of the loop is 1 m, the induced emf in the …

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on

Magnetic flux (in weber) in a closed circuit of resistance $20\Omega$ varies with time $t(s)$ as $\varphi =8t^2-9t+5$. The magnitude of the induced current at $t=0.25$ s will be ______ mA

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.)

A metallic rod of length 20 cm is palced in NorthSouth 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 …

The dimension of mutual inductance is :

Two coils of self inductance ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

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 $5\mathrm{rad}/\mathrm{s}$. If the horizontal component of earth's magnetic field is $0.2\times 10^{-4}\mathrm{T}$, then emf induced …

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\varphi =\left(5t^3+4t^2+2t-5\right)$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at $t=2\sec$ will be:

A $10\Omega ,20\mathrm{mH}$ coil carrying constant current is connected to a battery of 20 V through a switch is opened current becomes zero in $100\mu \mathrm{s}$. The average emf induced in the coil is ____ V.

A coil of inductance 1 H and resistance $100\Omega$ is connected to a battery of 6 V. Determine approximately :
(a) The time elapsed before the current acquires half of its steady - state value
(b) The energy stored in the magnetic field associated with the coil at an instant …

A circular coil of 1000 turns each with area $1{\mathrm{m}}^2$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07 T. The maximum voltage generation will be $\_\_\_\_$ V.

Match List-I with List-II

List-I
(A) AC generator
(B) Galvanometer
(C) Transformer
(D) Metal detector

List-II
(I) Shows deflection when current passes through it
(II) Converts mechanical energy into electrical energy
(III) Works on the principle of resonance in AC circuit
(IV) …

The current in a coil of self inductance 2.0 H is increasing according to $\mathrm{I}=2\sin ({\mathrm{t}}^2)$ A. The amount of energy spent during the period when current changes from 0 to 2 A is ______ J.

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 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 :

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of $50\mathrm{rad}{\mathrm{s}}^{-1}$ in a uniform horizontal magnetic field of $3.0\times 10^{-2}\mathrm{T}$. The maximum emf induced in the coil will be _____ …

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 $\mathrm{x}=0$ to $\mathrm{x}=\mathrm{b}$. Identify the graph the varia …

Figure shows a circuit that contains four identical resistors with resistance $\mathrm{R}=2.0\Omega$, two identical inductors with inductance $\mathrm{L}=2.0\mathrm{mH}$ and an ideal battery with emf $\mathrm{E}=9\mathrm{V}$. The current ' i ' just after switch ' $S$ ' is clo …

A constant magnetic field of 1 T is applied in the $\mathrm{x}>0$ region. A metallic circular ring of radius 1 m is moving with a constant velocity of $1\mathrm{m}/\mathrm{s}$ along the $x$-axis. At $t=0$, the centre of $O$ of the ring is at $x=-1\mathrm{m}$. What will be t …