The law of electromagnetic induction has been used in the construction of

Magnetic flux (in $Wb$) linked with a closed loop varies with time $t$ (in $s$) as $\phi = 2t^2 + 1$. The magnitude of induced emf at $t = 1 \ s$ is $..... \ V$.

Magnetic flux (in weber) in a closed circuit of resistance $20\,\Omega$ varies with time $t(s)$ as $\phi = 8t^2 - 9t + 5$. The magnitude of the induced current at $t = 0.25\,s$ will be $...mA$.

Consider a metal ring kept on top of a fixed solenoid (say on a cardboard) as per the figure. The center of the ring coincides with the axis of the solenoid. If the current is suddenly switched on,the metal ring jumps up. Explain.

$A$ magnet is brought towards a coil $(i)$ speedily and $(ii)$ slowly. What will be the induced $e.m.f.$ and induced charge, respectively?

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on