$A$ conducting wire is dropped along the east-west direction. Then,

$A$ 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? $(1 \; G = 10^{-4} \; T)$

$XPQY$ is a vertical smooth long loop having a total resistance $R$, where $PX$ is parallel to $QY$ and the separation between them is $l$. $A$ constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. $A$ rod $CD$ of length $L$ $(L > l)$ and mass $m$ is made to slide down from rest under gravity as shown in the figure. The terminal speed acquired by the rod is . . . . . . $m/s$. ($g$ = acceleration due to gravity)

An electric potential difference will be induced between the ends of the conductor shown in the diagram,when the conductor moves in the direction

$A$ bicycle wheel of radius $R$ has $n$ spokes. It is rotating at the rate of $F$ r.p.m. perpendicular to the horizontal component of earth's magnetic field $\vec{B}$. The e.m.f. induced between the rim and the centre of the wheel is

$A$ rectangular loop of length $l$ and breadth $b$ is placed at a distance of $x$ from an infinitely long wire carrying current $i$ such that the direction of the current is parallel to the breadth of the loop. If the loop moves away from the current-carrying wire in a direction perpendicular to it with a velocity $v$,the magnitude of the induced emf in the loop is: ($\mu_0=$ permeability of free space)