$A$ conducting rod is moving towards the right with a velocity '$V$' in a uniform magnetic field '$B$'. If the direction of the induced current '$i$' is as shown in the figure,then the direction of '$B$' is:

$(a)$ Obtain an expression for the mutual inductance between a long straight wire and a square loop of side $a$ as shown in Figure.
$(b)$ Now assume that the straight wire carries a current of $50\; A$ and the loop is moved to the right with a constant velocity, $v=10\; m / s$. Calculate the induced $emf$ in the loop at the instant when $x=0.2\; m$. Take $a=0.1\; m$ and assume that the loop has a large resistance.

$A$ straight conductor of length $0.4 \ m$ is moving with a speed of $7 \ ms^{-1}$ perpendicular to a magnetic field of intensity $0.9 \ Wb \ m^{-2}$. The induced emf across the conductor will be (in $V$)

The loops have lengths $L$ or $2L$. All loops enter a magnetic field $\vec{B}$ with the same velocity $v$. Which of the following is correct?

$A$ rectangular coil $ABCD$ is rotated anticlockwise with a uniform angular velocity about the axis shown in the diagram below. The axis of rotation of the coil as well as the magnetic field $B$ are horizontal. The induced $e.m.f.$ in the coil would be maximum when

$A$ wire of length $10 \, cm$ translates in a direction making an angle of $60^\circ$ with its length. The plane of motion is perpendicular to a uniform magnetic field of $1.0 \, T$ that exists in the space. Find the $emf$ induced between the ends of the rod if the speed of translation is $20 \, cm/s$.