$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

$A$ square loop of area $25 \, cm^2$ has a resistance of $10 \, \Omega$. The loop is placed in a uniform magnetic field of magnitude $40 \, T$. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1 \, s$ will be:

$A$ metal disc of radius $a = 10 \ cm$ rotates with a constant angular speed of $\omega = 200 \ rad \ s^{-1}$ about its axis. The potential difference between the centre and the rim of the disc under a uniform magnetic field $B = 5 \ mT$ directed perpendicular to the disc is: (in $mV$)

$A$ horizontal wire of mass $m$,length $l$,and resistance $R$ is sliding on vertical rails in a uniform magnetic field $B$ directed perpendicularly. The terminal speed of the wire as it falls under the force of gravity is ($g =$ acceleration due to gravity).

$A$ 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 . . . . . $\times 10^{-6} \, J$.

$A$ square loop $ABCD$ is moving with constant velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ which is perpendicular to the plane of paper and directed outward. The resistance of the coil is $R$. What is the rate of production of heat energy in the loop? [$L$ = length of side of the loop]