$A$ 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 (magnitude only):

What is the cause of the force acting on a sliding conductor placed in a magnetic field?

$A$ 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 $\mu_0 = 4 \pi \times 10^{-7} \ NA^{-2}$]

As shown in the figure,a metal rod makes contact and completes the circuit. The circuit is perpendicular to the magnetic field with $B = 0.15 \, T$. If the resistance is $3 \, \Omega$,the force needed to move the rod as indicated with a constant speed of $2 \, m/s$ is:

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, m/s$ perpendicular to a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a resistance of $6 \, \Omega$. The rate at which work is being done to keep the wire moving at that speed is:

An aircraft with a wing-span of $40\, m$ flies with a speed of $1080\, km\, h^{-1}$ in the eastward direction at a constant altitude in the northern hemisphere,where the vertical component of earth's magnetic field is $1.75 \times 10^{-5} \, T$. Then the emf that develops between the tips of the wings is.......$V$