In a circuit with a coil of resistance $2\, \Omega$,the magnetic flux changes from $2.0\, Wb$ to $10.0\, Wb$ in $0.2\, s$. The charge that flows in the coil during this time is..........$C$.

The figure shows a bar magnet and a metallic coil. Consider four situations:
$(I)$ Moving the magnet away from the coil.
$(II)$ Moving the coil towards the magnet.
$(III)$ Rotating the coil about the vertical diameter.
$(IV)$ Rotating the coil about its axis.
An emf in the coil will be generated for the following situations.

To induce an $e.m.f.$ in a coil, the linking magnetic flux

Two different loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop then,is

$A$ long solenoid with $15$ turns per $cm$ has a small loop of area $2.0 \,cm^2$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 \,A$ to $4.0 \,A$ in $0.1 \,s$, the induced emf in the loop while the current is changing is nearly [Take $\pi=3.14$].

$A$ wire of irregular shape is turning into a circular shape in a magnetic field which is directed into the paper. The direction of the induced current is