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A \( 1 \, \text{m} \) long metal rod \( AB \) completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of \( 0.10 \, \text{T} \). 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 \( 1.5 \, \text{m/s} \) is ______________ \( \text{N} \).

A capacitor \( C \) is first charged fully with potential difference of \( V_0 \) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance \( L \). In \( t \) \( \text{s} \) \( 25\% \) of the initial energy in the capacitor is transferred to the inductor. The value of \( t \) is ______ \( \text{s} \).

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 \( 3r \) 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 ______.

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 ________.

Figure shows the circuit that contains three resistances \(9 \, \Omega\) each and two inductors \((4 \, \text{mH}\) each). The reading of ammeter at the moment switch \( K \) is turned ON, is ________ \( \text{A} \).

In the given circuit below inductance values of \( L_{1} \), \( L_{2} \) and \( L_{3} \) are same. The magnetic energy stored in the entire circuit is \((U_t)\) and that stored in the \( L_{2} \) inductor is \((U_t)\). \( \dfrac{U_{t}}{U_{l}} \) is ______.
(Ignore the mutual inductance if any)

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 slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is _______ \( \text{m/s} \). (\( g = \) acceleration due to gravity)

A metal rod of length \( L \) rotates about one end at origin with a uniform angular velocity \( \omega \). The magnetic field radially falls off as \( B(r)=B_0 e^{-\lambda r} \), \( \lambda \) being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is:

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

A circular loop of radius \( 20 \, \text{cm} \) and resistance \( 2 \, \Omega \) is placed in a time varying magnetic field \( \vec{B} = (2t^{2} + 2t + 3)\,\text{T} \). At \( t = 0 \), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \( t = 3 \, \text{s} \) is \( \dfrac{\alpha}{50} \, \text{A} \). The value of \( \alpha \) is ____________. (Take \( \pi = \dfrac{22}{7} \))

Three identical coils \( C_1 \), \( C_2 \) and \( C_3 \) are closely placed such that they share a common axis. \( C_2 \) is exactly midway. \( C_1 \) carries current \( I \) in anti-clockwise direction while \( C_3 \) carries current \( I \) in clockwise direction. An induced current flows through \( C_2 \) will be in clockwise direction when:

A \( 20 \, \text{m} \) long uniform copper wire held horizontally is allowed to fall under the gravity \( (g = 10 \, \text{m/s}^{2}) \) through a uniform horizontal magnetic field of \( 0.5 \, \text{Gauss} \) perpendicular to the length of the wire. The induced EMF across the wire when it travels a vertical distance of \( 200 \, \text{m} \) is ______ mV.

A circular loop of radius \( 7 \, \text{cm} \) is placed in uniform magnetic field of \( 0.2 \, \text{T} \) directed perpendicular to plane of loop. The loop is converted into a square loop in \( 0.5 \, \text{s} \). The EMF induced in the loop is _______ \( \text{mV} \).

A conducting circular loop is rotated about its diameter at a constant angular speed of \( 100 \, \text{rad/s} \) in a magnetic field of \( 0.5 \, \text{T} \) perpendicular to the axis of rotation. When the loop is rotated by \( 30^\circ \) from the horizontal position, the induced EMF is \( 15.4 \, \text{mV} \). The radius of the loop is ______ mm. (Take \( \pi = \frac{22}{7} \))

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

A simple pendulum made of mass \( 10 \, \text{g} \) and a metallic wire of length \( 10 \, \text{cm} \) is suspended vertically in a uniform magnetic field of \( 2 \, \text{T} \). The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of \( 60^\circ \) with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ______ \( \text{mV} \). [Take \( g = 10 \, \text{m}/\text{s}^{2} \)]

An inductor of inductance \( 10 \, \text{mH} \) having resistance of \( 100\Omega \) is connected to battery of E.M.F. \( 1.0 \, \text{V} \) 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 \( 2 \, \text{mA} \) and \( 4 \, \text{mA} \) is _____.

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JEE Main 2026 22nd Jan Evening Shift

Figure shows the circuit that contains three resistances \(9 \, \Omega\) each and two inductors \((4 \, \text{mH}\) each). The reading of ammeter at the moment switch \( K \) is turned ON, is ________ \( \text{A} \).