$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced $emf$ in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.

$A$ metallic conductor of length $1 \; m$ rotates in a vertical plane parallel to the east-west direction about one of its ends with an angular velocity of $5 \; rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4} \; T$,then the emf induced between the two ends of the conductor is .............

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

$A$ wheel with $10$ metallic spokes,each $0.5 \; m$ long,is rotated with a speed of $120 \; rev/min$ in a plane normal to the horizontal component of the Earth's magnetic field $H_{E}$ at a place. If $H_{E} = 0.4 \; G$ at the place,what is the induced $emf$ between the axle and the rim of the wheel? $(1 \; G = 10^{-4} \; T)$

$A$ $800$ turn coil of effective area $0.05\; m^{2}$ is kept perpendicular to a magnetic field $5 \times 10^{-5}\; T$. When the plane of the coil is rotated by $90^{\circ}$ around any of its coplanar axes in $0.1\; s$,the $emf$ induced in the coil will be.....$V$

Two identical conductors $P$ and $Q$ are placed on two frictionless rails $R$ and $S$ in a uniform magnetic field directed into the plane. If $P$ is moved in the direction shown in the figure with a constant speed,then rod $Q$