$A$ wire of length $L$ having resistance $R$ falls from a height $\ell$ in the Earth's horizontal magnetic field $B$. The induced emf through the wire is ($g$ = acceleration due to gravity).

$A$ conducting rod $AB$ of length $l$ is projected on a frictionless frame $PSRQ$ with velocity $v_0$ in a uniform magnetic field $\vec{B}$ directed into the plane. The velocity of the rod after time $t$ is

The magnetic induction in the region between the pole faces of an electromagnet is $0.7 \ Wb/m^2$. The induced $e.m.f.$ in a straight conductor $10 \ cm$ long,moving perpendicular to the magnetic field with a velocity of $2 \ m/s$ (where the conductor is also perpendicular to the field and its velocity),is.......$V$.

$A$ pair of parallel conducting rails lie at a right angle to a uniform magnetic field of $2.0\, T$ as shown in the figure. Two resistors,$10\,\Omega$ and $5\,\Omega$,slide without friction along the rails. The distance between the conducting rails is $0.1\, m$. Then:

$A$ wire of length $10 \, cm$ translates in a direction making an angle of $60^\circ$ with its length. The plane of motion is perpendicular to a uniform magnetic field of $1.0 \, T$ that exists in the space. Find the $emf$ induced between the ends of the rod if the speed of translation is $20 \, cm/s$.

$A$ rod of length $1.0 \,m$ is rotated in a plane perpendicular to a uniform magnetic field of induction $0.25 \,T$ with a frequency of $12 \,rev/s$. The induced emf across the ends of the rod is (in $\,V$)