$A$ square frame of side $10\, cm$ and a long straight wire carrying current $1\, A$ are in the plane of the paper. Starting from close to the wire,the frame moves towards the right with a constant speed of $10\, ms^{-1}$ (see figure). The $e.m.f.$ induced at the time the left arm of the frame is at $x = 10\, cm$ from the wire is .....$\mu V$.

$A$ long rectangular conducting loop of width ' $\ell$ ',mass ' $m$ ' and resistance ' $R$ ' is placed partly in a perpendicular magnetic field ' $B$ '. It is pushed downwards with velocity ' $V$ ' so that it may continue to fall freely. The velocity ' $V$ ' is

$A$ square loop $PQRS$ having $10$ turns, area $3.6 \times 10^{-3} \, m^2$ and resistance $100 \, \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B=0.5 \, T$ as shown. Work done in pulling the loop out of the field in $1.0 \, s$ is . . . . . $\times 10^{-6} \, J$.

$A$ certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B = 0.8 \, T$. When released,the radius of the loop starts shrinking at a constant rate of $dr/dt = -2 \, cm/s$. The induced emf in the loop at an instant when the radius of the loop is $r = 10 \, cm$ will be $........ mV$.

$A$ thin strip $10\, cm$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5\, N/m$ (see figure). The assembly is kept in a uniform magnetic field of $0.1\, T$. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $e$ is $N$. If the mass of the strip is $50\, g$, its resistance $10\, \Omega$ and air drag is negligible, $N$ will be close to:

The figure shows an isosceles triangle wire frame with an apex angle equal to $\pi / 2$. The frame starts entering into the region of a uniform magnetic field $B$ with a constant velocity $v$ at $t = 0$. The longest side of the frame is perpendicular to the direction of velocity. If $i$ is the instantaneous current through the frame,then choose the alternative showing the correct variation of $i$ with time.