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The magnetic field in a region is given by \( \vec{B} = B_{0} \left( \dfrac{x}{a} \right) \hat{k} \). A square loop of side \( d \) is placed with its edges along the \( x \) and \( y \) axes. The loop is moved with a constant velocity \( \vec{v} = v_{0} \hat{i} \). The emf induced in the loop is:

Figure shows a circuit that contains four identical resistors with resistance \( R = 2.0 \, \Omega \), two identical inductors with inductance \( L = 20 \, \text{mH} \) and an ideal battery with emf \( E = 9 \, \text{V} \). The current ‘\( i \)’ just after the switch ‘\( S \)’ is closed will be:

A constant magnetic field of \( 1\,\text{T} \) is applied in the \( x > 0 \) region. A metallic circular ring of radius \( 1\,\text{m} \) is moving with a constant velocity of \( 1\,\text{m/s} \) along the \( x \)-axis. At \( t = 0\,\text{s} \), the centre \( O \) of the ring is at \( x = -1\,\text{m} \). What will be the value of the induced emf in the ring at \( t = 1\,\text{s} \)? (Assume the velocity of the ring does not change)

A square loop of side \( 20 \, \text{cm} \) and resistance \( 1 \, \Omega \) is moved towards right with a constant speed \( v_0 \). The right arm of the loop is in a uniform magnetic field of \( 5 \, \text{T} \). The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value \( 4 \, \Omega \). What should be the value of \( v_0 \) so that a steady current of \( 2 \, \text{mA} \) flows in the loop?

For the given circuit the current \( i \) through the battery when the key in closed and the steady state has been reached is:

For the given circuit, comment on the type of transformer used.

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 \(x = 0\) to \(x = b\). Identify the graph showing the variation of different quantities with distance.

A bar magnet is passing through a conducting loop of radius \( R \) with velocity \( v \). The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve:

A coil is placed in a magnetic field \( \vec{B} \) as shown below:

A current is induced in the coil because \( \vec{B} \) is:
A current is induced in the coil because \( \vec{B} \) is:

A circular coil of radius \( 8.0 \, \text{cm} \) \( 20 \) turns is rotated about its vertical diameter with an angular speed of \( 50 \, \text{rad s}^{-1} \) in a uniform horizontal magnetic field of \( 3.0 \times 10^{-2} \, \text{T} \). The maximum emf induced the coil will be __________ \( \times 10^{-2} \) volt (rounded off to the nearest integer).

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

A circular conducting coil of radius \( 1 \, \text{m} \) is being heated by the change of magnetic field \( \vec{B} \) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is \( 2 \, \mu \Omega \). The magnetic field is slowly switched off such that its magnitude changes in time as \( B = \dfrac{4}{\pi} \times 10^{-3} \, \text{T} \left( 1 - \dfrac{t}{100} \right) \). The energy dissipated by the coil before the magnetic field is switched off completely is \( E = \) __________ \( \text{m} \)).

For a series LCR circuit with \( R = 100\,\Omega \), \( L = 0.5\,\text{mH} \) and \( C = 0.1\,\text{pF} \) connected across \( 220\,\text{V} - 50\,\text{Hz} \) AC supply, the phase angle between current and supplied voltage and the nature of the circuit is:

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is \( 3 \, \text{T} \), the field at the center of C would be:
(Assume that the magnetic field is confined with in the volume of respective solenoid).

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then \( T_1 \) is connected to \( T_2 \). As the current in \( R = 6 \, \Omega \) attains a maximum value of steady state level, \( T_1 \) is disconnected from \( T_2 \) and immediately connected to \( T_3 \). Potential drop across \( r = 3 \, \Omega \) resistor immediately after \( T_1 \) is connected to \( T_3 \) is _______ \( \text{V} \). (Round off to the Nearest Integer)

In the given figure the magnetic flux through the loop increases according to the relation \( \phi_{B}(t) = 10 t^{2} + 20 t \), where \( \phi_{B} \) is in milliwebers and \( t \) is in seconds. The magnitude of current through \( R = 2 \, \Omega \) resistor at \( t = 5 \, \text{s} \) is __________ \( \text{mA} \).

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JEE Main 2021 1st September Evening Shift

For the given circuit the current \( i \) through the battery when the key in closed and the steady state has been reached is: