We know from Faraday's Law of Electromagnetic Induction that due to Time Varying Magnetic Field (TVMF), a non conservative electric field will be induced.
Now if we consider a cylindrical region in which the magnetic field is varying with time then outside the region of cylinder there is no magnetic field and no variation of it either, so how does the electric field gets induced there?
I understand that in the interiority of the cylindrical region, the electric field will be induced as there is TVMF, but how it gets induced outside it?
Isn't it true that Induced electric field should only generate at the location of time variation of magnetic field?
Isn't it strange TVMF can produce Induced Electric Field even at a distant location?
Is it a law of nature kind of thing that TVMF can produce induce electric field at a distant location?