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

$A$ long rectangular conducting loop of width '$l$',mass '$m$',and resistance '$R$' is placed partly in a perpendicular magnetic field '$B$'. With what velocity should it be pushed downwards so that it may continue to fall without any acceleration? ($g = $ acceleration due to gravity)

If a wheel with $24$ metallic spokes each $40 \ cm$ long is rotated with a speed of $180 \ rev/min$ in a plane normal to the horizontal component of earth's magnetic field, the emf induced between the axle and the rim of the wheel is $E$. If the number of spokes is made $12$ and the wheel is rotated with a speed of $90 \ rev/min$ in the same field, the induced emf is

Refer to the figure. The arm $PQ$ of the rectangular conductor is moved from $x=0$ outwards. The uniform magnetic field is perpendicular to the plane and extends from $x=0$ to $x=b$ and is zero for $x>b$. Only the arm $PQ$ possesses substantial resistance $r$. Consider the situation when the arm $PQ$ is pulled outwards from $x=0$ to $x=2b$ and is then moved back to $x=0$ with constant speed $v$. Obtain expressions for the flux,the induced emf,the force necessary to pull the arm,and the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

$A$ conducting rod $PQ$ of length $l = 5 \ m$ is oriented as shown in the figure. It is moving with a velocity $\vec{V} = (2 \ m/s) \hat{i}$ without any rotation in a uniform magnetic field $\vec{B} = (3 \hat{j} + 4 \hat{k}) \ T$. The induced $Emf$ in the rod is...........$V$.

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the magnitude of potential differences.