$A$ horizontal loop $abcd$ is moved across the pole pieces of a magnet as shown in the figure with a constant speed $v$. When the edge $ab$ of the loop enters the pole pieces at time $t = 0 \text{ s}$,which one of the following graphs correctly represents the induced emf in the coil?

$A$ boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5} \text{ T}$ due north and horizontal. The boat carries a vertical conducting rod $2 \text{ m}$ long. If the speed of the boat is $2.00 \text{ m/s}$, the magnitude of the induced e.m.f. in the rod is: (in $\text{ mV}$)

$A$ straight conductor of length $0.4\;m$ is moved with a speed of $7\;m/s$ perpendicular to a magnetic field of intensity $0.9\;Wb/m^2$. The induced $e.m.f.$ across the conductor will be......$V$.

To measure a magnetic field between the magnetic poles of a loudspeaker, a small coil having $30$ turns and $2.5 \, cm^2$ area is placed perpendicular to the field and removed immediately. If the total charge flown through the coil is $7.5 \times 10^{-3} \, C$ and the total resistance of the wire and galvanometer is $0.3 \, \Omega$, then the magnitude of the magnetic field is

An aeroplane is travelling horizontally towards west with a speed of $540 \,km/h$. The wing span of the plane is $20 \,m$. If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$, the potential difference developed between the ends of the wing is (in $\,V$)

$A$ metal disc of radius $30 \ cm$ rotates with a constant angular velocity $\omega = 100 \ rad/s$ about its axis. Find the magnitude of the potential difference between the centre and the rim of the disc if an external uniform magnetic field of induction $B = 4 \ mT$ is directed perpendicular to the disc. (in $mV$)