$A$ conducting rod $AB$ of length $l = 1\,m$ is moving with a velocity $v = 4\,m/s$. The velocity vector makes an angle of $30^o$ with the length of the rod. $A$ uniform magnetic field $B = 2\,T$ exists in a direction perpendicular to the plane of motion. Then:

$A$ long,rectangular conducting loop of width $l$,mass $m$,and resistance $R$ is placed partly in a perpendicular magnetic field $B$. It is pushed downwards with velocity $v$ so that it may continue to fall freely. The velocity $v$ is ($g=$ acceleration due to gravity).

When a rod of length $l$ is rotated with angular velocity $\omega$ in a uniform magnetic field of induction $B$ perpendicular to the plane of rotation,about one of its ends,the induced emf across its ends is:

$A$ rectangular loop is provided with a sliding connector of length $1 \, m$ and resistance $2 \, \Omega$. It is placed in a uniform magnetic field of $2 \, T$ perpendicular to the plane of the loop. The external force required to keep the connector moving with a uniform velocity of $2 \, ms^{-1}$ is: (in $N$)

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 wire is dropped along the east-west direction. Then,