$A$ square-shaped wire loop of mass $m$,resistance $R$,and side $a$ moving with speed $v_{0}$,parallel to the $X$-axis,enters a region of uniform magnetic field $B$,which is perpendicular to the plane of the loop. The speed of the loop changes with distance $x$ $(x < a)$ in the field as:

$A$ conducting rod of length $L$ rotates with angular speed $\omega$ in a uniform magnetic field of induction $B$ which is perpendicular to its motion. The induced emf developed between the two ends of the rod is

$A$ 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 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 ....... $V$.

$A$ 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.......$C$

$A$ wheel of radius $2 \, m$ having $8$ conducting concentric spokes is rotating about its geometrical axis with an angular velocity of $10 \, rad \, s^{-1}$ in a uniform magnetic field of $0.2 \, T$ perpendicular to its plane. The value of induced emf between the rim of the wheel and the centre is . . . . . . $V$.