$A$ metal disc of radius $a = 10 \ cm$ rotates with a constant angular speed of $\omega = 200 \ rad \ s^{-1}$ about its axis. The potential difference between the centre and the rim of the disc under a uniform magnetic field $B = 5 \ mT$ directed perpendicular to the disc is: (in $mV$)

When a wire loop is rotated in a magnetic field,the direction of induced $e.m.f.$ changes once in each........$revolution$.

$A$ copper rod of mass $m$ slides under gravity on two smooth parallel rails,with separation $l$ and set at an angle of $\theta$ with the horizontal. At the bottom,the rails are joined by a resistance $R$. There is a uniform magnetic field $B$ normal to the plane of the rails,as shown in the figure. The terminal speed of the copper rod is

$A$ thin wire of length $2\,m$ is placed perpendicular to the $x-y$ plane. It is moved with velocity $\overrightarrow v = (2\hat i + 3\hat j + \hat k)\,m/s$ through a region of magnetic induction $\overrightarrow B = (\hat i + 2\hat j)\,Wb/m^2$. The potential difference induced between the ends of the wire is......$V$.

$A$ fighter plane of length $20\, m$, wing span (distance from tip of one wing to the tip of the other wing) of $15\,m$ and height $5\,m$ is flying towards east over Delhi. Its speed is $240\, ms^{-1}$. The earth's magnetic field over Delhi is $5 \times 10^{-5}\,T$ with the declination angle $\, 0^\circ$ and dip of $\theta$ such that $\sin \theta = 2/3$. If the voltage developed is $V_B$ between the lower and upper side of the plane and $V_W$ between the tips of the wings, then $V_B$ and $V_W$ are close to:

$A$ rod of length $20 \text{ cm}$ is rotating with an angular speed of $100 \text{ rps}$ in a magnetic field of strength $0.5 \text{ T}$ about one of its ends. What is the potential difference between the two ends of the rod? $(V)$