$A$ 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:

$A$ simple pendulum made of a mass of $10 \ g$ and a metallic wire of length $10 \ cm$ is suspended vertically in a uniform magnetic field of $2 \ T$. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ}$ with the vertical, then the maximum induced $EMF$ between the point of suspension and the point of oscillation is . . . . . . $mV$. (Take $g = 10 \ m/s^2$)

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement$(s)$ from the following.

The figure shows four wire loops,with edge lengths of either $L$ or $2L$. All four loops move through a region of uniform magnetic field (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the electromotive force (e.m.f.) induced as they move through the field,greatest first.

$A$ wire of length $1\, m$ is perpendicular to the $x-y$ plane. It is moved with velocity $\vec{v} = (3\hat{i} + 3\hat{j} + 2\hat{k})\, m/s$ through a region of uniform magnetic field $\vec{B} = (\hat{i} + 2\hat{j})\, T$. The potential difference between the ends of the wire is (in $V$):

$A$ wheel with $20$ metallic spokes,each $1 \,m$ long,is rotated with a speed of $120 \,rpm$ in a plane perpendicular to a magnetic field of $0.4 \,G$. The induced emf between the axle and the rim of the wheel will be $\left(1 \;G = 10^{-4} \;T \right)$.