$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced $emf$ in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement$(s)$ from the following.

The loop shown moves with a velocity $v$ in a uniform magnetic field of magnitude $B$,directed into the paper. The potential difference between $P$ and $Q$ is $e$. Then:

$A$ 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:

The direction of current induced in a wire moving in a magnetic field is found using

$A$ circular conducting coil of radius $1\, m$ is being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\, \mu\Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as $B = \frac{4}{\pi} \times 10^{-3} T \left(1 - \frac{t}{100}\right)$. The energy dissipated by the coil before the magnetic field is switched off completely is $E = .....\, mJ$.