$A$ conductor $10 \ cm$ long is moved with a speed $1 \ m/s$ perpendicular to a magnetic field of strength $1000 \ A/m$. The e.m.f. induced in the conductor is [Given : $\mu_0 = 4 \pi \times 10^{-7} \ Wb/Am$]

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 $B$.

$A$ straight wire of length $L$ is bent into a semicircle. It is moved in a uniform magnetic field with speed $v$ with its diameter perpendicular to the field. The induced emf between the ends of the wire is

Two $U$-shaped tubes are moving inside each other as shown in the figure. If the length of each tube is $l$ and they move with velocity $v$ in a magnetic field $B$,what is the induced $emf$ in the circuit?

$A$ rectangular wire loop of sides $5 \text{ cm}$ and $3 \text{ cm}$ with a small cut is moving away from an infinitely long straight wire carrying a current of $30 \text{ A}$ with a velocity of $20 \text{ ms}^{-1}$ as shown in the figure. The emf induced across the cut is (in $\mu V$)

$A$ rod of $10 \ cm$ length is moving perpendicular to a uniform magnetic field of intensity $5 \times 10^{-4} \ Wb/m^2$. If the acceleration of the rod is $5 \ m/s^2$, then the rate of increase of induced $emf$ is . . . . . . .