$A$ 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).

$A$ 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 $mV$)

If a wheel with $24$ metallic spokes each $40 \ cm$ long is rotated with a speed of $180 \ rev/min$ in a plane normal to the horizontal component of earth's magnetic field, the emf induced between the axle and the rim of the wheel is $E$. If the number of spokes is made $12$ and the wheel is rotated with a speed of $90 \ rev/min$ in the same field, the induced emf is

$A$ wire $cd$ of length $l$ and mass $m$ is sliding without friction on conducting rails $ax$ and $by$ as shown. The vertical rails are connected to each other with a resistance $R$ between $a$ and $b$. $A$ uniform magnetic field $B$ is applied perpendicular to the plane $abcd$ such that $cd$ moves with a constant velocity $v$. Find the value of $v$.

$A$ 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.

Two straight conducting rails form a right angle as shown below. $A$ conducting bar in contact with the rails starts at the vertex at time $t=0$ and moves with a constant velocity of $v=5 \ m \ s^{-1}$ along them. $A$ magnetic field with $B=0.1 \ T$ is directed out of the page. The absolute value of the emf induced in the circuit at time $t=4 \ s$ will be (in $V$)?