Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ rotate uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

$A$ rectangular loop $PQMN$ with a movable arm $PQ$ of length $12 \, cm$ and resistance $2 \, \Omega$ is placed in a uniform magnetic field of $0.1 \, T$ acting perpendicular to the plane of the loop as shown in the figure. The resistance of the arms $MN$, $NP$, and $MQ$ are negligible. The current induced in the loop when arm $PQ$ is moved with a velocity of $20 \, ms^{-1}$ is (in $ \, A$)

$A$ wheel of $20$ metallic spokes, each $40 \text{ cm}$ long, is rotated with a speed of $180 \text{ rev/min}$ in a plane normal to the horizontal component of Earth's magnetic field $H_{e}$ at a place. If $H_{e} = 0.4 \text{ G}$ at that place, the induced emf between the axle and the rim of the wheel is:

$A$ metal conductor of length $1 \ m$ rotates vertically about one of its ends at 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 e.m.f. developed between the two ends of the conductor is:

The magnetic induction in the region between the pole faces of an electromagnet is $0.7 \ Wb/m^2$. The induced $e.m.f.$ in a straight conductor $10 \ cm$ long,moving perpendicular to the magnetic field with a velocity of $2 \ m/s$ (where the conductor is also perpendicular to the field and its velocity),is.......$V$.

$A$ circular coil of radius $30 \ cm$,having $1$ turn and a resistance of ${\pi ^2} \ \Omega$,is placed in a magnetic field of $10^{-2} \ T$. The coil rotates about its diameter with a speed of $200 \ rpm$ in a direction perpendicular to the magnetic field. The value of the induced $AC$ current in the coil will be . . . . . . $mA$.