Question

why is magnetic flux created due to change in electric flux ?

Answer 1

There is no answer to 'why'
It is just one of the facts of the universe. It is just like asking, why masses create gravity? or why masses curve the space time..
or why all subatomic particles have intrinsic spin?
or why all of them have a fundamental charge?

So time changing magnetic flux can induce an electric FIELD and a time changing electric flux can induce a magnetic field is one of those fundamental facts of this universe!
it can be proved to be true
it can be made use of
but answer 'why' it is true is just not possible!

Answer 2

Physics has no answers as to why things happen but just informs our observations and tells us HOW. From this we create laws.

This is quite different from mathematics that has Theorems. Proven to be true forever. And we know why. In Physics we call them "Laws" because they are consistent with our observations but are not proofs. One point of difference I make with @Mashy is that these Laws can and have been changed based on new knowledge; so in a sense Laws are not proven but are just deemed consistent with current observations. Look at how Newton's Laws were tweaked once we understood Special Relativity.

This is actually one of the more troubling aspects of physics in my opinion. We use physics to understand and to make things. But it ends there, unfortunately.

Maybe your question is not why, but how:

$$
\oint_{\partial \Sigma} \mathbf{H} \cdot \mathrm{d}\boldsymbol{\ell} = \iint_{\Sigma} \mathbf{J}_\text{f} \cdot \mathrm{d}\mathbf{S} + \frac{d}{dt} \iint_{\Sigma} \mathbf{D} \cdot \mathrm{d}\mathbf{S}
$$
That last integral basically says that the change in Electric Flux through a Closed surface will induce an EMF. This was Maxwell's contribution to Ampere's Law to explain how a changing electric flux can induce a magnetic field and helped him explain how current could flow through a capacitor even though there were no actual charges going across the plates. Again, it tells us that this does occur, but not why.

Answer 3

I think you made a mistake in your last sentence

"a change in electric flux through an OPEN SURFACE will induce a MAGNETIC field"

Answer 4

@Mashy - Thanks! You are correct. It is Gauss's Law that requires the Closed Surface, while Ampere's Law requires the Open Surface.

Answer 5

Ampere Maxwell's law :D :D