$A$ horizontal straight wire $5 \ m$ long extending from east to west is falling freely at a right angle to the horizontal component of the earth's magnetic field $0.60 \times 10^{-4} \ Wb \ m^{-2}$. The instantaneous value of the emf induced in the wire when its velocity is $10 \ m \ s^{-1}$ is . . . . . . $\times 10^{-3} \ V$.

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 $\rho$.)

Explain the motional $emf$ by the Lorentz force acting on the free charge carriers of a conductor.

$A$ coil of mean area $500 \ cm^2$ and having $1000$ turns is held with its plane perpendicular to a uniform magnetic field of $0.4 \ G$. If the coil is turned through $180^{\circ}$ in $\frac{1}{10} \ s$,then the average induced emf is $(1 \ G = 10^{-4} \ T)$. (in $V$)

Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time $t=0$,its left arm passes the origin,$O$. If for $t \geq 0$,the current in the loop is $I$ and the distance of its left arm from the origin is $x$,then $I$ versus $x$ graph will be

The figure shows a straight wire placed between the pole pieces of a magnet. An induced emf will be developed across the ends of the wire when it is moved towards: