$A$ rod of length $2 \, m$ slides with a speed of $5 \, ms^{-1}$ on a rectangular conducting frame as shown in the figure. There exists a uniform magnetic field of $0.04 \, T$ perpendicular to the plane of the figure. If the resistance of the rod is $3 \, \Omega$, the current through the rod is

$A$ coil of area $80 \, cm^2$ and $50$ turns is rotating with $2000$ revolutions per minute about an axis perpendicular to a magnetic field of $0.05 \, T$. The maximum value of the e.m.f. developed in it is

$A$ conducting wire is moving towards the right in a magnetic field $B$. The direction of the induced current $i$ in the wire is shown in the figure. The direction of the magnetic field will be

$A$ rectangular loop with a sliding connector of length $l = 1.0 \, m$ is situated in a uniform magnetic field $B = 2 \, T$ perpendicular to the plane of the loop. The resistance of the connector is $r = 2 \, \Omega$. Two resistors of $6 \, \Omega$ and $3 \, \Omega$ are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity $v = 2 \, m/s$ is ........ $N$.

$A$ uniform magnetic field exists in the region given by $\vec{B} = 3\hat{i} + 4\hat{j} + 5\hat{k} \, T$. $A$ rod of length $L = 5 \, m$ placed along the $y$-axis is moved along the $x$-axis with a constant speed $v = 1 \, ms^{-1}$. The induced e.m.f. in the rod is ......... $V$.

$A$ $20\,cm$ long metallic rod is rotated with $210\,rpm$ 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 $0.2\,T$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is $.......\,mV$. Take $\pi=\frac{22}{7}$.