$A$ horizontal wire is free to slide on the vertical rails of a conducting frame as shown in the figure. The wire has a mass $m$ and length $l$,and the resistance of the circuit is $R$. If a uniform magnetic field $B$ is directed perpendicular to the frame,find the terminal speed of the wire as it falls under the force of gravity.

$A$ rectangular wire loop of sides $5 \text{ cm}$ and $3 \text{ cm}$ with a small cut is moving away from an infinitely long straight wire carrying a current of $30 \text{ A}$ with a velocity of $20 \text{ ms}^{-1}$ as shown in the figure. The emf induced across the cut is (in $\mu V$)

$A$ $1.0 \; m$ long metallic rod is rotated with an angular frequency of $400 \; rad \; s^{-1}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. $A$ constant and uniform magnetic field of $0.5 \; T$ parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring. (in $; V$)

The figure shows an isosceles triangle wire frame with an apex angle equal to $\pi / 2$. The frame starts entering into the region of a uniform magnetic field $B$ with a constant velocity $v$ at $t = 0$. The longest side of the frame is perpendicular to the direction of velocity. If $i$ is the instantaneous current through the frame,then choose the alternative showing the correct variation of $i$ with time.

When a rod of length $l$ is rotated with angular velocity $\omega$ in a uniform magnetic field of induction $B$ perpendicular to the plane of rotation,about one of its ends,the induced emf across its ends is:

$A$ wheel with $10$ metallic spokes,each $0.5 \; m$ long,is rotated with a speed of $120 \; rev/min$ in a plane normal to the horizontal component of the Earth's magnetic field $H_{E}$ at a place. If $H_{E} = 0.4 \; G$ at the place,what is the induced $emf$ between the axle and the rim of the wheel? $(1 \; G = 10^{-4} \; T)$