why does change in magnetic flux induce current and vice versa?
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It’s less that it induces current, but rather they’re really the same thing. It’s not electricity and magnetism, but electromagnetism. It’s like if you splash water and create a wave, the splashing doesn’t really create the wave, the moving of the water is the wave.
Let’s start with vice-versa, because it’s actually the fundamental one.
A moving or changing electric field produces a magnetic field. It’s just how electromagnetism fundamentally works. And has to do with changing frames of reference (in the context of Special Relativity, i.e. Einstein) and how the components of electromagnetism appear to us when viewed from those frames of references. If you don’t know what reference frames, special relativity or Lorentz transforms are, just go with the first two sentences.
An electron produces an electric field, so if we see it moving, we will see a magnetic field produced. Electricity is moving electrons, therefore an electric current creates a magnetic field.
Inducing current with magnetic fields works because if an electron moves through a magnetic field, it’s path is bent. But since movement is relative, a magnetic field moving or changing around an electron will cause the same force to act on it as if the electron was moving through a stationary field. Again, because electricity is electrons moving, moving an electron induces current. Therefore moving or changing magnetic fields create electricity.
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