The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \ T$ and the dip is $\tan^{-1}(4/3)$. $A$ thin metal rod of length $0.25 \ m$ placed in the north-south position is moved at a constant speed of $10 \ cm/s$ towards the east. Find the $e.m.f.$ induced in the rod across its ends in $\mu V$.

Two metallic rings of radius $R$ are rolling on a metallic rod. $A$ magnetic field of magnitude $B$ is applied in the region. The magnitude of the potential difference between point $A$ and point $C$ on the two rings (as shown) will be:

$A$ thin wire of length $2 \ m$ is perpendicular to the $xy$-plane. It moves with a velocity $v = (2\hat{i} + 3\hat{j} + \hat{k}) \ m/s$ in a magnetic field $B = (\hat{i} + 2\hat{j}) \ Wb/m^2$. What is the induced potential difference (emf) across the ends of the wire?

$A$ frame $CDEF$ is placed in a region where a magnetic field $\vec{B}$ is present. $A$ rod $PQ$ of length $l = 1 \, m$ moves with a constant velocity $v = 20 \, m/s$ and the strength of the magnetic field is $B = 1 \, T$. The power spent in the process is .............. $kW$ (take $R = 0.2 \, \Omega$ and assume all other wires and the rod have zero resistance).

$A$ conducting rod is moving in a uniform magnetic field as shown in the diagram. Which end is at a lower potential?

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity. If the wire $AB$ is replaced by a semicircular wire,the magnitude of the induced current will