$A$ rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \, \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are:

$A$ conductor of length $l$ and mass $m$ can slide along a pair of vertical metal guides connected by a resistance $R$,as shown in the figure. Friction,resistance of the conductor,and guide rails are negligible. There exists a horizontal uniform magnetic field of strength $B$ normal to the plane of the page and directed outward. The terminal speed of fall under the influence of gravity is:

$A$ square loop $PQRS$ having $10$ turns, area $3.6 \times 10^{-3} \, m^2$ and resistance $100 \, \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B=0.5 \, T$ as shown. Work done in pulling the loop out of the field in $1.0 \, s$ is . . . . . $\times 10^{-6} \, J$.

$A$ rectangular loop circuit has a sliding wire $PQ$ as shown in the figure. The loop is placed in a magnetic field $B$,perpendicular to its plane. The resistance of the wire $PQ$ is $R$. If the wire moves with constant velocity $v$,then find the current flowing in the wire $PQ$?

$A$ coil of area $10 \ m^2$ is placed in a uniform magnetic field of $0.3 \ Wb \cdot m^{-2}$,with its plane perpendicular to the field. The coil rotates at a uniform rate to complete one revolution in $8 \ s$. Find the average emf (in $V$) in the coil during intervals when the coil rotates from:
$i. 0^{\circ}$ to $90^{\circ}$ position
$ii. 90^{\circ}$ to $180^{\circ}$ position
$iii. 180^{\circ}$ to $270^{\circ}$ position
$iv. 270^{\circ}$ to $360^{\circ}$ position

$A$ conducting circular loop is placed in a uniform magnetic field of $0.04\, T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of $2\, mm/s$. The induced $emf$ in the loop when the radius is $2\, cm$ is: