$A$ conducting circular loop is placed in a uniform magnetic field,$B = 0.025 \, T$,with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of $1 \, mm \, s^{-1}$. The induced $emf$ when the radius is $2 \, cm$ is:

$A$ rectangular wire loop of sides $8 \;cm$ and $2 \;cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \;T$ directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 \;cm \,s^{-1}$ in a direction normal to the $(a)$ longer side,$(b)$ shorter side of the loop? For how long does the induced voltage last in each case?

$A$ 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 $\mu V$)

$A$ straight conductor of length $0.4\;m$ is moved with a speed of $7\;m/s$ perpendicular to a magnetic field of intensity $0.9\;Wb/m^2$. The induced $e.m.f.$ across the conductor will be......$V$.

$A$ conducting rod of length $l$ moves with a constant velocity $\upsilon$ perpendicular to a long,straight wire carrying a current $I$,as shown in the figure. Calculate the $emf$ generated between the ends of the rod.

$A$ circular conducting coil of radius $1\, m$ is being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\, \mu\Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as $B = \frac{4}{\pi} \times 10^{-3} T \left(1 - \frac{t}{100}\right)$. The energy dissipated by the coil before the magnetic field is switched off completely is $E = .....\, mJ$.