The figure shows a bar magnet and a metallic coil. Consider four situations:
$(I)$ Moving the magnet away from the coil.
$(II)$ Moving the coil towards the magnet.
$(III)$ Rotating the coil about the vertical diameter.
$(IV)$ Rotating the coil about its axis.
An emf in the coil will be generated for the following situations.

If a coil of $40$ turns and area $4 \, cm^2$ is suddenly removed from a magnetic field,it is observed that a charge of $2 \times 10^{-4} \, C$ flows through the coil. If the resistance of the coil is $80 \, \Omega$,the magnetic flux density in $Wb \, m^{-2}$ is:

$A$ magnetic field $B$ is confined to a region $r \le a$ and points out of the paper (the $z$-axis),$r = 0$ being the centre of the circular region. $A$ charged ring (charge $= Q$) of radius $b$,$b > a$ and mass $m$ lies in the $xy$-plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time $\Delta t$. Find the angular velocity $\omega$ of the ring after the field vanishes.

$A$ rectangular coil of $20$ turns and area of cross section $25 \text{ cm}^2$ has a resistance of $100 \Omega$. If a magnetic field which is perpendicular to the plane of the coil changes at a rate of $100 \text{ T/s}$, the current in the coil is . . . . . . . (in $\text{ A}$)

$A$ space consists of two uniform magnetic fields,as shown. $A$ conducting circular loop is placed symmetrically at the boundary.

Lenz's law is representing which fundamental conservation law?