$A$ $10\,m$ long horizontal wire extends from North-East to South-West. It is falling with a speed of $5.0\,m/s$,at right angles to the horizontal component of the earth's magnetic field,which is $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced $emf$ in the wire is:

Statement-$I$: When a conducting rod moves in a uniform transverse magnetic field with a uniform speed which is perpendicular to its length,then a potential difference may develop across its ends.
Statement-$II$: In any conductor,free electrons and free positive ions are available.

$A$ long horizontal metallic rod with length along the east-west direction is falling under gravity. The potential difference between its two ends will

Derive the expression for the mechanical power required to move a conducting rod of length $l$ with a constant velocity $v$ in a uniform magnetic field $B$.

$A$ square conducting frame of side $a$ and a long straight wire carrying current $I$ are placed as shown in the figure. If the frame is moved to the right with a constant velocity $V$,then the induced $emf$ in the frame is proportional to:

$A$ fixed rectangular conductor $ODBAC$ has negligible resistance (where $CO$ is not connected). $A$ conductor $OP$ rotates clockwise with an angular velocity $\omega$ as shown in the figure. The entire system is in a uniform magnetic field $B$ directed along the normal to the surface of the rectangular conductor $ABDC$. The conductor $OP$ is in electric contact with $ABDC$. The rotating conductor has a resistance of $\lambda$ per unit length. Find the current in the rotating conductor as it rotates by $180^{\circ}$.