(A) For the wire to reach terminal velocity,its acceleration must be zero.At terminal velocity,the magnetic force acting upwards must balance the grav

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(A) For the wire to reach terminal velocity,its acceleration must be zero.At terminal velocity,the magnetic force acting upwards must balance the gravitational force acting downwards.$F_m = mg$$I l B = mg$Since the induced electromotive force $(EMF)$ is $\varepsilon = B l v_0$,where $v_0$ is the terminal velocity,the induced current $I$ is given by:$I = \frac{\varepsilon}{R} = \frac{B l v_0}{R}$Substituting this into the force balance equation:$\left( \frac{B l v_0}{R} \right) l B = mg$$\frac{B^2 l^2 v_0}{R} = mg$Solving for $v_0$:$v_0 = \frac{mgR}{B^2 l^2}$

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ horizontal wire is free to slide on the vertical rails of a conducting frame as shown in the figure. The wire has a mass $m$ and length $l$,and the resistance of the circuit is $R$. If a uniform magnetic field $B$ is directed perpendicular to the frame,find the terminal speed of the wire as it falls under the force of gravity.

A
$\frac{mgR}{B^2l^2}$
B
$\frac{mg}{Bl}$
C
$\frac{2mgR}{B^2l^2}$
D
$0$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

$A$ closed loop is moving with constant velocity in a uniform magnetic field as shown. The potential difference and current in element $AB$ will be:

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$A$ certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B = 0.8 \, T$. When released,the radius of the loop starts shrinking at a constant rate of $dr/dt = -2 \, cm/s$. The induced emf in the loop at an instant when the radius of the loop is $r = 10 \, cm$ will be $........ mV$.

MediumJEE MAIN 2023

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$A$ wire of mass $m$ and length $l$ can slide freely on a pair of smooth,vertical rails (figure). $A$ magnetic field $B$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance $C$. The acceleration of the wire,neglecting any electric resistance,is:

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$A$ rectangular coil of single turn,having area $A$,rotates in a uniform magnetic field $B$ with an angular velocity $\omega$ about an axis perpendicular to the field. If initially the plane of the coil is perpendicular to the field,then the average induced $e.m.f.$ when it has rotated through $90^{\circ}$ is

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Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity. If the wire $AB$ is replaced by a semicircular wire,the magnitude of the induced current will

EasyAP EAMCET 2020

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$A$ closed loop is moving with constant velocity in a uniform magnetic field as shown. The potential difference and current in element $AB$ will be:

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity. If the wire $AB$ is replaced by a semicircular wire,the magnitude of the induced current will

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