Faraday's laws are a consequence of the conservation of

$A$ long solenoid has $20$ turns per cm. $A$ small loop of area $\frac{4}{\pi} \text{ cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $1.0 \text{ A}$ to $3.0 \text{ A}$ in $0.2 \text{ s}$,what is the magnitude of the induced emf in the loop while the current is changing (in $\mu \text{V}$)?

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 $.... \, J$.

The magnetic flux through a loop of resistance $10 \Omega$ varies according to the relation $\phi = 6t^2 + 7t + 1$,where $\phi$ is in milliweber and time is in seconds. At time $t = 1 \ s$,the induced e.m.f. is:

$A$ long solenoid having $100$ turns per $cm$ carries a current of $\frac{4}{\pi} \,A$. At the centre of it is placed a coil of $200$ turns of cross-sectional area $25 \,cm^2$ having its axis parallel to the field produced by the solenoid. When the direction of the current in the solenoid is reversed within $0.04 \,s$, the induced emf in the coil is (in $\,V$)

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.