$A$ conducting circular loop is placed in a uniform magnetic field of $0.04\, T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of $2\, mm/s$. The induced $emf$ in the loop when the radius is $2\, cm$ is:

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

$A$ metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_0 e^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

$A$ conducting rod of length $L$ lies in the $XY$-plane and makes an angle $30^{\circ}$ with the $X$-axis. One end of the rod is initially at the origin. $A$ magnetic field exists in the region pointing along the positive $Z$-direction. The magnitude of the magnetic field varies with $y$ as $B = B_0 \left(\frac{y}{L}\right)^3$,where $B_0$ is a constant. At some instant,the rod starts moving with a velocity $v_0$ along the $X$-axis. The emf induced in the rod is

$A$ circular coil of radius $10 \, cm$ and resistance of $2 \, \Omega$ is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in $0.25 \, s$. If the magnitude of the induced emf is $3.8 \times 10^{-3} \, V$, then the number of turns of the coil is (Horizontal component of earth's magnetic field at the place is $3 \times 10^{-5} \, T$) (in $turns$)

The figure shows an apparatus suggested by Faraday to generate electric current from a flowing river. Two identical conducting plates of length $a$ and width $b$ are placed parallel facing one another on opposite sides of the river flowing with velocity $u$ at a distance $d$ apart. Now both the plates are connected by a load resistance $R$. Then the current through the load $R$ is: (Consider the vertical component of the magnetic field produced by the earth is $B_v$ and the resistivity of river water is $\rho$.)