$A$ coil of resistance $400\,\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in $Wb$) linked with the coil varies with time $t$ (in $s$) as $\phi = 50t^2 + 4$,the current in the coil at $t = 2\,s$ is $..........\,A$.

$A$ circular coil of area $2 \text{ cm}^2$ is placed in a magnetic field of $3 \text{ T}$ perpendicularly. The coil has $10$ turns and $5 \text{ } \Omega$ resistance. Now,the coil is removed from the magnetic field in $0.2 \text{ s}$. The value of induced charge flowing through the coil is . . . . . . .

On which factor does the induced charge depend?

The magnetic field of an electromagnetic wave in a certain region obeys the relation $B = 10^{-12} \sin(5 \times 10^6 t) \text{ T}$,where $t$ is the time. Then,the induced emf in a coil of $300$ turns and area $20 \text{ cm}^2$,oriented perpendicular to the field,is:

Assertion : Lenz's law violates the principle of conservation of energy.
Reason : Induced $emf$ always opposes the change in magnetic flux responsible for its production.

The magnetic flux through a coil of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$. The total quantity of induced electric charge $Q$ is