$A$ vertical bar magnet is dropped from the shown position on the axis of a fixed metallic coil as shown in Fig-$I$. In Fig-$II$,the magnet is fixed and a horizontal coil is dropped. If the acceleration of the magnet and coil are $a_1$ and $a_2$ respectively,then:

$A$ magnet is moved towards a stationary coil with speed $V$. The induced e.m.f. in the coil is $e$. If the magnet and the coil move away from one another,each moving with speed $V$,then the induced e.m.f. in the coil is:

The coil of a dynamo is rotating in a magnetic field. The developed induced $e.m.f.$ changes and the number of magnetic lines of force also changes. Which of the following conditions is correct?

$A$ coil has an area of $0.05\, m^2$ and it has $800$ turns. It is placed perpendicularly in a magnetic field of strength $4 \times 10^{-5}\, Wb/m^2$. It is rotated through $90^o$ in $0.1\, s$. The average $e.m.f.$ induced in the coil is (in $, V$)

$A$ closed planar wire loop of area $A$ and arbitrary shape is placed in a uniform magnetic field of magnitude $B$,with its plane perpendicular to the magnetic field. The resistance of the wire loop is $R$. The loop is now turned upside down by $180^o$ so that its plane again becomes perpendicular to the magnetic field. The total charge that must have flowed through the wire ring in the process is

The magnetic flux linked with a coil varies as $\phi = 3t^{2} + 4t + 9$. The magnitude of the emf induced at $t = 2 \text{ s}$ is: (in $\text{ V}$)