$A$ 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 .....$\mu V$.

$A$ wire of length $L$ having resistance $R$ falls from a height $\ell$ in the Earth's horizontal magnetic field $B$. The induced emf through the wire is ($g$ = acceleration due to gravity).

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 $\rho$.)

$A$ long metal rod of length $L$ completes the circuit as shown. The area of the circuit is perpendicular to the magnetic field $B$. The total resistance of the circuit is $R$. The force needed to move the rod in the direction as shown with a constant speed $V$ is:

$A$ copper rod of mass $m$ slides under gravity on two smooth parallel rails,with separation $l$ and set at an angle of $\theta$ with the horizontal. At the bottom,the rails are joined by a resistance $R$. There is a uniform magnetic field $B$ normal to the plane of the rails,as shown in the figure. The terminal speed of the copper rod is

$A$ square frame of metallic wire is moving in a uniform magnetic field $(\vec{B})$ acting perpendicular to the paper inward as shown. $LP$ and $QN$ are also metallic wires. Find the potential difference between $L$ and $N$.