$A$ metallic wire loop of side $l = 0.1 \text{ m}$ and resistance $1 \Omega$ is moved with a constant velocity in a uniform magnetic field of $2 \text{ Wb m}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of the loop required to have a steady current of $1 \text{ mA}$ in the loop is: (in $\text{ cm s}^{-1}$)

$A$ 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 $E = .....\, mJ$.

$A$ solid metal cube of edge length $2\, cm$ is moving in a positive $y-$ direction at a constant speed of $6\, m/s$. There is a uniform magnetic field of $0.1\, T$ in the positive $z-$ direction. The potential difference between the two faces of the cube perpendicular to the $x-$ axis is.....$mV$.

$A$ rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the $x$-axis with a constant velocity $v_0$ in the plane of the paper. At $t=0$,the right edge of the loop enters a region of length $3L$ where there is a uniform magnetic field $B$ into the plane of the paper,as shown in the figure. For sufficiently large $v_0$,the loop eventually crosses the region. Let $x$ be the location of the right edge of the loop. Let $v(x)$,$I(x)$,and $F(x)$ represent the velocity of the loop,current in the loop,and force on the loop,respectively,as a function of $x$. Counter-clockwise current is taken as positive. Which of the following schematic plot$(s)$ is(are) correct? (Ignore gravity)

$A$ metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region,the $e.m.f.$ induced across the ends of the rod is

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is: