$A$ jet plane of wing span $20 \,m$ is travelling towards west at a speed of $400 \,ms^{-1}$. If the earth's total magnetic field is $4 \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$ at that place, the voltage difference developed across the ends of the wing is (in $\,V$)

The figure shows a square loop of side $5 \, cm$ being moved towards the right at a constant speed of $1 \, cm/s$. The front edge enters the $20 \, cm$ wide magnetic field at $t = 0$. Find the magnitude of the $emf$ induced in the loop at $(a) \, t = 2 \, s$, $(b) \, t = 10 \, s$, and $(c) \, t = 22 \, s$.

$A$ metal rod of length $1\,m$ is rotated about one of its ends in a plane at right angles to a magnetic field of induction $2.5 \times 10^{-3}\,Wb/m^2$. If it makes $1800\,rpm$,calculate the induced e.m.f. between its ends in $V$.

Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side $a$ initially. $A$ uniform magnetic field $B$ exists at right angles to the plane containing the conductors. They all start moving outwards with a constant velocity $v$. If $r$ is the resistance per unit length of the wire,the current in the circuit will be

Figure $(i)$ shows a conducting loop being pulled out of a magnetic field with a speed $v$. Which of the four plots shown in figure $(ii)$ may represent the power delivered by the pulling agent as a function of the speed $v$?

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