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 $Q$

$A$ 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 . . . . . . $\times 10^{-3} \ V$.

$A$ horizontal straight wire $10 \; m$ long extending from east to west is falling with a speed of $5.0 \; m \, s^{-1}$,at right angles to the horizontal component of the earth's magnetic field,$0.30 \times 10^{-4} \; Wb \, m^{-2}$.
$(a)$ What is the instantaneous value of the $emf$ induced in the wire?
$(b)$ What is the direction of the $emf$?
$(c)$ Which end of the wire is at the higher electrical potential?

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the potential of the points $P, Q$ and $R$.

$A$ circular coil of $500$ turns encloses an area of $0.04 \,m^2$. $A$ uniform magnetic field of induction $0.25 \,Wb/m^2$ is applied perpendicular to the plane of the coil. The coil is rotated by $90^o$ in $0.1 \,s$ at a constant angular velocity about one of its diameters. $A$ galvanometer of resistance $25 \,\Omega$ is connected in series with the coil. The total charge that will pass through the galvanometer is.......$C$

An aeroplane in which the distance between the tips of wings is $50 \ m$ is flying horizontally with a speed of $360 \ km/hr$ over a place where the vertical component of the Earth's magnetic field is $2.0 \times 10^{-4} \ Wb/m^2$. The potential difference between the tips of the wings would be $V$.