$A$ metal disc of radius $30 \ cm$ rotates with a constant angular velocity $\omega = 100 \ rad/s$ about its axis. Find the magnitude of the potential difference between the centre and the rim of the disc if an external uniform magnetic field of induction $B = 4 \ mT$ is directed perpendicular to the disc. (in $mV$)

$A$ rod of length $1.0 \,m$ is rotated in a plane perpendicular to a uniform magnetic field of induction $0.25 \,T$ with a frequency of $12 \,rev/s$. The induced emf across the ends of the rod is (in $\,V$)

$A$ conducting square loop of side $l$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. $A$ magnetic induction $B$ constant in time and space,pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field,as shown in figure. The induced $e.m.f.$ is

$A$ $20 \ m$ long uniform copper wire held horizontally is allowed to fall under gravity $(g = 10 \ m/s^2)$ through a uniform horizontal magnetic field of $0.5 \ Gauss$ perpendicular to the length of the wire. The induced $EMF$ across the wire after it travels a vertical distance of $200 \ m$ is . . . . . . $mV$.

$A$ player with a $3 \text{ m}$ long iron rod runs towards the east with a speed of $30 \text{ km/hr}$. The horizontal component of the Earth's magnetic field is $4 \times 10^{-5} \text{ Wb/m}^2$. If the player is running with the rod in horizontal and vertical positions,then the potential difference induced between the two ends of the rod in the two cases will be:

$A$ metallic cube of side $15\,cm$ is moving along the $y$-axis at a uniform velocity of $2\,m/s$ in a region of uniform magnetic field of magnitude $0.5\,T$ directed along the $z$-axis. In equilibrium,the potential difference between the faces of higher and lower potential developed because of the motion through the field will be $..........mV$.