An aircraft of wing span $40 \ m$ flies horizontally in the Earth's magnetic field of $5 \times 10^{-5} \ T$ at a speed of $500 \ m/s$. The electromotive force (e.m.f.) generated between the tips of the wings of the aircraft is: (in $V$)

$A$ conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure. Two resistors $R_{1}$ and $R_{2}$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$. The correct statement about the directions of induced currents $I_{1}$ and $I_{2}$ flowing through $R_{1}$ and $R_{2}$ respectively is:

The current-carrying wire and the rod $AB$ are in the same plane. The rod moves parallel to the wire with a velocity $v$. Which one of the following statements is true about the induced emf in the rod?

$A$ $10 \, m$ wire kept in the east-west direction is falling with a velocity of $5 \, m/s$ perpendicular to the magnetic field of $0.3 \times 10^{-4} \, Wb/m^2$. The induced e.m.f. across the terminals of the wire will be:

$A$ square loop of side $a$ and resistance $R$ is moved in a region of uniform magnetic field $B$ (the loop remaining completely inside the field) with a velocity $v$ through a distance $x$. The work done is:

$A$ very small circular loop of radius $a$ is initially (at $t=0$) coplanar and concentric with a much larger fixed circular loop of radius $b$. $A$ constant current $I$ flows in the larger loop. The smaller loop is rotated with a constant angular speed $\omega$ about the common diameter. The emf induced in the smaller loop as a function of time $t$ is