$A$ rod of length $20 \text{ cm}$ is rotating with an angular speed of $100 \text{ rps}$ in a magnetic field of strength $0.5 \text{ T}$ about one of its ends. What is the potential difference between the two ends of the rod? $(V)$

$A$ conducting circular loop is placed in a uniform magnetic field of $0.04\, T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of $2\, mm/s$. The induced $emf$ in the loop when the radius is $2\, cm$ is:

$A$ conducting square loop of side $l$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. $A$ magnetic induction $B$ constant in time and space,pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field,as shown in figure. The induced $e.m.f.$ is

$A$ long,rectangular conducting loop of width $l$,mass $m$,and resistance $R$ is placed partly in a perpendicular magnetic field $B$. It is pushed downwards with velocity $v$ so that it may continue to fall freely. The velocity $v$ is ($g=$ acceleration due to gravity).

$A$ train with an axle of length $1.66 \ m$ is moving towards north with a speed of $90 \ km/h$. If the vertical component of the earth's magnetic field is $0.2 \times 10^{-4} \ T$,the emf induced across the ends of the axle of the train is: (in $mV$)

The direction of current induced in a wire moving in a magnetic field is found using