$A$ metallic disc of radius $0.3 \ m$ is rotating with a constant angular speed of $60 \ rad \ s^{-1}$ in a plane perpendicular to a uniform magnetic field of $5 \times 10^{-2} \ T$. The emf induced between a point on the rim and the centre of the disc is: (in $V$)

$A$ straight conductor $0.1 \ m$ long moves in a uniform magnetic field of $0.1 \ T$. The velocity of the conductor is $15 \ m/s$ and is directed perpendicular to the field. The emf induced between the two ends of the conductor is: (in $V$)

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.

$A$ metallic rod of length $1 \,m$ held along the east-west direction is allowed to fall down freely. Given the horizontal component of the Earth's magnetic field $B_H = 3 \times 10^{-5} \,T$. The emf induced in the rod at an instant $t = 2 \,s$ after it is released is (Take $g = 10 \,m/s^2$):

$A$ wire $ab$ of length $l$,mass $m$,and resistance $R$ slides on a smooth,thick pair of metallic rails joined at the bottom as shown in the figure. The plane of the rails makes an angle $\theta$ with the horizontal. $A$ vertical magnetic field $B$ exists in the region. If the wire slides on the rails at a constant speed $v$,then which of the following can be correct for $B$?

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $v$ in a uniform magnetic field $B$ directed into the plane of the paper (See figure). If charge densities $\sigma_1$ and $\sigma_2$ are induced on the left and right surfaces,respectively,of the sheet,then (ignore fringe effects):