$A$ metal conductor of length $1 \ m$ rotates vertically about one of its ends at an angular velocity of $5 \ rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4} \ T$,then the e.m.f. developed between the two ends of the conductor is:

$A$ metallic wire loop of side $l = 0.1 \text{ m}$ and resistance $1 \Omega$ is moved with a constant velocity in a uniform magnetic field of $2 \text{ Wb m}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of the loop required to have a steady current of $1 \text{ mA}$ in the loop is: (in $\text{ cm s}^{-1}$)

$A$ thin semicircular conducting ring of radius $R$ is falling with its plane vertical in a horizontal magnetic induction $B$. At the position $MNQ$,the speed of the ring is $V$ and the potential difference developed across the ring is

The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. $A$ uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b$. Identify the graph showing the variation of different quantities with distance.

$A$ horizontal telegraph wire of length $30 \ m$ spread east to west falls freely from a height of $20 \ m$. If the resistance of the wire is $40 \ \Omega$ and the horizontal component of the earth's magnetic field at the place is $2 \times 10^{-5} \ T$,then the induced current when the wire reaches the ground is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

$A$ square frame of metallic wire is moving in a uniform magnetic field $(\vec{B})$ acting perpendicular to the paper inward as shown. $LP$ and $QN$ are also metallic wires. Find the potential difference between $L$ and $N$.