$A$ metal rod of length $l$ rotates about one of its ends in a plane perpendicular to a magnetic field of induction $B$. If the e.m.f. induced between the ends of the rod is $e$,then the number of revolutions made by the rod per second is:

The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \ T$ and the dip is $\tan^{-1}(4/3)$. $A$ thin metal rod of length $0.25 \ m$ placed in the north-south position is moved at a constant speed of $10 \ cm/s$ towards the east. Find the $e.m.f.$ induced in the rod across its ends in $\mu V$.

The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \, T$ and the angle of dip is $53^\circ$. $A$ metal rod of length $0.25 \, m$ is placed in the north-south position and is moved at a constant speed of $10 \, cm/s$ towards the east. The emf induced in the rod will be ...... $\mu V$. (Given $\tan 53^\circ = 4/3$)

$A$ horizontal straight wire $20 \; m$ long extending from east to west is falling with a speed of $5.0 \; m/s$ at right angles to the horizontal component of the earth's magnetic field $0.30 \times 10^{-4} \; Wb/m^2$. The instantaneous value of the emf induced in the wire will be ......... $mV$.

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform magnetic field $B$ directed into the plane of the paper (See figure). If charge densities $\sigma_1$ and $\sigma_2$ are induced on the left and right surfaces,respectively,of the sheet,then (ignore fringe effects):

$A$ constant force $F$ is applied to a conducting rod of length $l$ moving with constant speed $V$ on two parallel conducting rails connected at the ends by a resistance $R$ in a uniform magnetic field $B$,as shown. If the current flowing through the circuit is $I$,then: