$A$ jet plane having a wing span of $25 \ m$ is travelling horizontally towards the east with a speed of $3600 \ km/h$. If the Earth's magnetic field at the location is $4 \times 10^{-4} \ T$ and the angle of dip is $30^{\circ}$,then the potential difference between the ends of the wing is: (in $V$)

$A$ conducting square loop of side $l$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. $A$ magnetic induction $B$ constant in time and space,pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field,as shown in figure. The induced $e.m.f.$ is

$A$ rectangular conducting loop of length $4 \ cm$ and width $2 \ cm$ is in the $xy$-plane,as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2} \hat{x} + \frac{1}{2} \hat{y}$ with a constant speed $v$. The wire is carrying a steady current $I = 10 \ A$ in the positive $x$-direction. $A$ current of $10 \ \mu A$ flows through the loop when it is at a distance $d = 4 \ cm$ from the wire. If the resistance of the loop is $0.1 \ \Omega$,then the value of $v$ is. . . . . . $ms^{-1}$.
[Given: The permeability of free space $\mu_0 = 4 \pi \times 10^{-7} \ NA^{-2}$]

$A$ bar of mass $m$,length $d$,and resistance $R$ slides without friction in a horizontal plane,moving on parallel rails as shown in the figure. $A$ battery that maintains a constant emf $\varepsilon$ is connected between the rails,and a constant magnetic field $\vec{B}$ is directed perpendicularly to the plane of the page. Assuming the bar starts from rest,find the speed at time $t$.

$A$ metallic rod of length '$L$' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field '$B$' about an axis passing through one end of the rod,as shown in the figure. The induced emf will be:

$A$ square loop of side $15 \ cm$ is being moved towards the right at a constant speed of $2 \ cm/s$ as shown in the figure. The front edge enters the $50 \ cm$ wide magnetic field region at $t=0$. The value of the induced emf in the loop at $t=10 \ s$ will be: