Consider a metal ball of radius $r$ moving at a constant velocity $v$ in a uniform magnetic field of induction $\vec{B}$. Assuming that the direction of velocity forms an angle $\alpha$ with the direction of $\vec{B}$,the maximum potential difference between points on the ball is

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is:

$A$ coil of area $10 \ m^2$ is placed in a uniform magnetic field of $0.3 \ Wb \cdot m^{-2}$,with its plane perpendicular to the field. The coil rotates at a uniform rate to complete one revolution in $8 \ s$. Find the average emf (in $V$) in the coil during intervals when the coil rotates from:
$i. 0^{\circ}$ to $90^{\circ}$ position
$ii. 90^{\circ}$ to $180^{\circ}$ position
$iii. 180^{\circ}$ to $270^{\circ}$ position
$iv. 270^{\circ}$ to $360^{\circ}$ position

$A$ $1.0 \ m$ metallic rod is rotated with an angular frequency $200 \ rad \ s^{-1}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. $A$ constant and uniform magnetic field of $0.5 \ T$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is . . . . . . . (in $V$)

$A$ 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).

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