$A$ 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 . . . . . . $V$.

Derive the equation for the induced $emf$ in a rod of length $l$ sliding with velocity $v$ on a $U$-shaped frame placed perpendicular to a uniform magnetic field $B$.

Out of the following given loops, in which loop is the direction of the induced current from $a \rightarrow c \rightarrow b$?

$A$ 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

$A$ 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.

$A$ 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 $\text{ cm s}^{-1}$)