(B) The motional emf induced in the loop is given by: $V = B v l$.The current $i$ in the loop is given by Ohm's law: $i = \frac{V}{R} = \frac{B v l}{R

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(B) The motional emf induced in the loop is given by: $V = B v l$.The current $i$ in the loop is given by Ohm's law: $i = \frac{V}{R} = \frac{B v l}{R}$.As the loop falls,it experiences a magnetic force $F_m = i l B$ acting upwards. For the loop to fall with a constant terminal velocity $v$,the magnetic force must balance the gravitational force $mg$ acting downwards.Therefore,$i l B = m g$.Substituting the expression for $i$:$B \left( \frac{B v l}{R} \right) l = m g$$\frac{B^2 l^2 v}{R} = m g$$v = \frac{m g R}{B^2 l^2}$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ long,rectangular conducting loop of width $l$,mass $m$,and resistance $R$ is placed partly in a perpendicular magnetic field $B$. It is pushed downwards with velocity $v$ so that it may continue to fall freely. The velocity $v$ is ($g=$ acceleration due to gravity).

MHT CET 2022 All MHT CET

A
$\frac{m g R^2}{B l}$
B
$\frac{m g R}{B^2 l^2}$
C
$\frac{m g l}{B^2 R^2}$
D
$\frac{B^2 l^2 R}{m g}$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

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$A$ square frame of side $10\, cm$ and a long straight wire carrying current $1\, A$ are in the plane of the paper. Starting from close to the wire,the frame moves towards the right with a constant speed of $10\, ms^{-1}$ (see figure). The $e.m.f.$ induced at the time the left arm of the frame is at $x = 10\, cm$ from the wire is .....$\mu V$.

MediumJEE MAIN 2014

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$A$ long,rectangular conducting loop of width $l$,mass $m$,and resistance $R$ is placed partly in a perpendicular magnetic field $B$. It is pushed downwards with velocity $v$ so that it may continue to fall freely. The velocity $v$ is ($g=$ acceleration due to gravity).

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$A$ jet plane is travelling towards west at a speed of $1800\; km/h$. What is the voltage difference developed between the ends of the wing having a span of $25\; m$,if the Earth's magnetic field at the location has a magnitude of $5 \times 10^{-4}\; T$ and the dip angle is $30^{\circ}$ (in $; V$)?

$A$ long rectangular conducting loop of width ' $\ell$ ',mass ' $m$ ' and resistance ' $R$ ' is placed partly in a perpendicular magnetic field ' $B$ '. It is pushed downwards with velocity ' $V$ ' so that it may continue to fall freely. The velocity ' $V$ ' is

$A$ $10 \, m$ wire kept in the east-west direction is falling with a velocity of $5 \, m/s$ perpendicular to the magnetic field of $0.3 \times 10^{-4} \, Wb/m^2$. The induced e.m.f. across the terminals of the wire will be:

Two $U$-shaped tubes are moving inside each other as shown in the figure. If the length of each tube is $l$ and they move with velocity $v$ in a magnetic field $B$,what is the induced $emf$ in the circuit?

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