$A$ rod of length $60 \ cm$ rotates with a uniform angular velocity $20 \ rad \ s^{-1}$ about its perpendicular bisector in a uniform magnetic field of $0.5 \ T$. The direction of the magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is . . . . . . $V$.

$A$ very small circular loop of radius $a$ is initially (at $t=0$) coplanar and concentric with a much larger fixed circular loop of radius $b$. $A$ constant current $I$ flows in the larger loop. The smaller loop is rotated with a constant angular speed $\omega$ about the common diameter. The emf induced in the smaller loop as a function of time $t$ is

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed is:

$A$ rod of length $l$,mass $m$,and resistance $R$ slides without friction down parallel conducting rails as shown in the figure. The rails are connected together at the bottom. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform vertical magnetic field $B$ exists throughout the region. Then the induced $emf$ in the loop,at the time the rod slides down with a speed $v$,is

$A$ metal disc rotates freely between the poles of a magnet in the direction indicated. Brushes $P$ and $Q$ make contact with the center (axle) and the edge of the disc,respectively. What current,if any,flows through $R$?

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 2\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\,\mu F$ is connected as shown in the figure. Then