$A$ wire of length $1\, m$ is perpendicular to the $x-y$ plane. It is moved with velocity $\vec{v} = (3\hat{i} + 3\hat{j} + 2\hat{k})\, m/s$ through a region of uniform magnetic field $\vec{B} = (\hat{i} + 2\hat{j})\, T$. The potential difference between the ends of the wire is (in $V$):

The wing span of an aeroplane is $20$ $m$. It is flying in a field where the vertical component of the Earth's magnetic field is $5 \times 10^{-5} \, T$,with a velocity of $360 \, km/h$. The potential difference produced between the wing tips will be ....... $V$.

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

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is:

$A$ conducting circular loop is rotated about its diameter at a constant angular speed of $100 \ rad/s$ in a magnetic field of $0.5 \ T$ perpendicular to the axis of rotation. When the loop is rotated by $30^{\circ}$ from the horizontal position, the induced $EMF$ is $15.4 \ mV$. The radius of the loop is . . . . . . $mm$. (Take $\pi = 22/7$)

The figure shows four wire loops,with edge lengths of either $L$ or $2L$. All four loops move through a region of uniform magnetic field (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the electromotive force (e.m.f.) induced as they move through the field,greatest first.