$A$ bar magnet is passing through a conducting loop of radius $R$ with velocity $v$. The radius of the bar magnet is such that it just passes through the loop. The induced $e.m.f.$ in the loop can be represented by the approximate curve:

Write the equation for the induced charge.

In a coil of resistance $8 \, \Omega$,the magnetic flux due to an external magnetic field varies with time as $\phi = \frac{2}{3}(9 - t^2)$. The value of total heat produced in the coil,till the flux becomes zero,will be $.... \, J$.

$A$ coil of resistance $200 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the coil varies with time $t$ (in second) as per the equation $\phi = 50t^2 + 4$,then the current induced in the coil at a time $t = 2 \ s$ is (in $A$)

As shown in the figure, two identical conducting rings of radius $r$ are placed in a magnetic field. In figure $(a)$, the magnetic field is increasing at the rate of $0.3 \text{ T/s}$, and in figure $(b)$, the magnetic field is decreasing at the rate of $0.2 \text{ T/s}$. The direction of the current in ring $(a)$ and ring $(b)$, when observed from the top, is . . . . . .

The direction of induced current is such that it opposes the very cause that has produced it. This is the law of