The magnetic flux linked with a coil satisfies the relation $\phi = 4t^2 + 6t + 9 \text{ Wb}$, where $t$ is the time in seconds. The emf induced in the coil at $t = 2 \text{ s}$ is (in $\text{ V}$)

The magnetic flux through a coil of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$. The amount of induced current and induced charge in the coil are respectively:

The adjoining figure shows two different arrangements in which two square wire frames are placed in a uniform constantly decreasing magnetic field $B.$ The direction of induced current in the case $II$ is

The north and south poles of two identical magnets approach a coil,containing a condenser,with equal speeds from opposite sides. Then

$A$ square loop of wire,side length $10 \, cm$,is placed at an angle of $45^{\circ}$ with a magnetic field that changes uniformly from $0.1 \, T$ to zero in $0.7 \, s$. The induced current in the loop (its resistance is $1 \, \Omega$) is ..... $mA$.

$A$ 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