$A$ rectangular loop circuit has a sliding wire $PQ$ as shown in the figure. The loop is placed in a magnetic field $B$,perpendicular to its plane. The resistance of the wire $PQ$ is $R$. If the wire moves with constant velocity $v$,then find the current flowing in the wire $PQ$?

$A$ $1.0 \; m$ 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 $; V$)

$A$ boy is playing with the empty rim of a cycle wheel of radius $40 \, cm$ by rolling it along a horizontal road towards north with an angular speed of $20 \, rad \, s^{-1}$. Considering the effect of the magnetic field of the Earth, the e.m.f. induced in the rim is (Horizontal component of Earth's magnetic field $= 0.26 \, G$)

Find the current in the wire for the configuration shown in the figure. Wire $PQ$ has negligible resistance. $\vec{B}$ is the magnetic field coming out of the paper. $\theta$ is a fixed angle made by $PQ$ as it travels smoothly over two conducting parallel wires separated by a distance $d$.

When a metal rod of length $l$ is placed in a magnetic field $B$ and moved with velocity $v$ perpendicular to the field,then the induced emf across its ends is

$A$ rectangular coil $ABCD$ is rotated in a uniform magnetic field with constant angular velocity $\omega$ about one of its diameters as shown in the figure. The induced $emf$ will be maximum when the plane of the coil is