$A$ $1\,m$ long metal rod $XY$ completes the circuit as shown in the figure. The plane of the circuit is perpendicular to the magnetic field of flux density $0.15\,T$. If the resistance of the circuit is $5\,\Omega$,the force needed to move the rod in the direction indicated with a constant speed of $4\,m/s$ will be $................\,10^{-3}\,N$.

$A$ rod of length $60 \ cm$ rotates with a uniform angular velocity $20 \ rad \ s^{-1}$ about its perpendicular bisector in a uniform magnetic field of $0.5 \ T$. The direction of the magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is . . . . . . $V$.

At a place,the value of the horizontal component of the Earth's magnetic field $H$ is $3 \times 10^{-5} \, Wb/m^2$. $A$ metallic rod $AB$ of length $2 \, m$,placed in the east-west direction with end $A$ towards the east,falls vertically downward with a constant velocity of $50 \, m/s$. Which end of the rod becomes positively charged,and what is the value of the induced potential difference between the two ends?

Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time $t=0$,its left arm passes the origin,$O$. If for $t \geq 0$,the current in the loop is $I$ and the distance of its left arm from the origin is $x$,then $I$ versus $x$ graph will be

$A$ metal wire of length $2500 \ m$ is kept in east-west direction,at a certain height from the ground. If it falls freely on the ground,then the current induced in the wire when its speed is $10 \ m/s$ is (Resistance of wire $= 25 \ \Omega$,$g = 10 \ m/s^2$ and Earth's horizontal component of magnetic field $B_{H} = 2 \times 10^{-5} \ T$). (in $A$)

$A$ $1.0 \ m$ 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 $V$)