$A$ long rectangular conducting loop of width ' $\ell$ ',mass ' $m$ ' and resistance ' $R$ ' is placed partly in a perpendicular magnetic field ' $B$ '. It is pushed downwards with velocity ' $V$ ' so that it may continue to fall freely. The velocity ' $V$ ' is

An aeroplane is travelling horizontally towards west with a speed of $540 \,km/h$. The wing span of the plane is $20 \,m$. If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$,the potential difference developed between the ends of the wing is (in $\,V$)

$A$ rectangular loop with a sliding connector of length $10\, cm$ is situated in a uniform magnetic field perpendicular to the plane of the loop. The magnetic induction is $0.1\, T$ and the resistance of the connector is $1\, \Omega$. The sides $AB$ and $CD$ have resistances $2\, \Omega$ and $3\, \Omega$ respectively. Find the current in the connector during its motion with a constant velocity of $1\, m/s$.

$A$ wire of length $L$ is bent into a semicircle and moved with a velocity $v$ in a magnetic field $B$ as shown. What is the induced $emf$ between its two ends?

$A$ metal disc of radius $30 \ cm$ rotates with a constant angular velocity $\omega = 100 \ rad/s$ about its axis. Find the magnitude of the potential difference between the centre and the rim of the disc if an external uniform magnetic field of induction $B = 4 \ mT$ is directed perpendicular to the disc. (in $mV$)

There is a uniform magnetic field $B$ normal to the $xy$ plane. $A$ conductor $ABC$ has length $AB = l_1$,parallel to the $x$-axis,and length $BC = l_2$,parallel to the $y$-axis. $ABC$ moves in the $xy$ plane with velocity $\vec{v} = v_x \hat{i} + v_y \hat{j}$. The potential difference between $A$ and $C$ is proportional to