Question

Faraday's law is the consequence of what?

Answer 1

A consequence of this effect is the fact that you can rotate a magnet in such a way as to cause current to flow in a wire, or even more, in a coil of wire. This is the means that generation of electric power is achieved.
It should be noted that the notations and concepts of vector calculus were not really existent at the time of these discoveries, and what seem like obvious consequences to us, given Stokes' theorem and the concept of the curl of a vector, were very obscure through most of the ${19}^{th}$ Century.
If we apply Stokes' theorem to the electric field E here, we can replace the right hand side here by -c multiplied by the flux of the curl of E. If we fix a surface S, the derivative can be brought inside the integral and we obtain, for any fixed surface S
$\int {\int }_s(\frac{B}{t}+cV\times E)dS=0$
If we make the physical assumption that a quantity that is 0 when its component in any direction is integrated over any surface is in fact always 0, we get the differential equation
$\frac{1}{c}\frac{B}{t}+V\times E=0$
and this can be considered as a mere restatement of Faraday's Law.
This law does not directly imply that there are no magnetic charges, that serve as "sources" for the magnetic field the way positive electric charges are "sources" and negative charges are "sinks" for the electric field.