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As light is electromagnetic radiation. Then why I don't see any magnet bending light wave? Or why light doesn't diffract whenever it passes by a live wire?

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In vacuum electromagnetic fields obey superposition to a very high degree of accuracy. A magnetic field does not have any effect on light. Light in material media can be affected by a magnetic field. This is known as the Kerr effect.

As for current carrying wires, these reflect and diffract electromagnetic waves like any metallic or dielectric object. This is why you see them. However, there is no effect of the current until the wire heats up.

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Electromagnetic fields simply superpose. They don’t interact with each other. (I am ignoring quantum effects at enormous field strengths.) Two waves go right through each other. A wave goes right through a static field.

Electromagnetic fields interact with charges. No charge, no interaction.

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    $\begingroup$ Then what about the second case in which light passes by a live wire. Here charges are certainly present. $\endgroup$
    – user238719
    Commented Oct 9, 2019 at 4:47
  • $\begingroup$ Wires are electrically neutral, so any interaction of waves with them is small. There is a proton for every electron, and they are very close together. $\endgroup$
    – G. Smith
    Commented Oct 9, 2019 at 4:52
  • $\begingroup$ What happens with enourmous field strengths? That means black holes and neutron stars, right? $\endgroup$
    – ikrase
    Commented Oct 9, 2019 at 5:44
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    $\begingroup$ @ikrase No. See en.wikipedia.org/wiki/Schwinger_limit, en.wikipedia.org/wiki/Two-photon_physics, and home.cern/news/news/physics/…. $\endgroup$
    – G. Smith
    Commented Oct 9, 2019 at 5:47
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    $\begingroup$ I meant "are these fields produced in practice by astrophysical objects", not "gravity". $\endgroup$
    – ikrase
    Commented Oct 9, 2019 at 5:51
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Roughly speaking, electric fields push and pull charges, while magnetic fields cause charges to loop around (by 'loop around' I'm saying that the magnetic fields cause the charges to accelerate at a right angle to their direction of motion).

Since light doesn't have an electric charge, there is nothing for electric fields to push or pull and nothing for magnetic fields to loop around.

If we just look at the classical case, then there is no direct interaction between magnetic fields and the electromagnetic wave. It's a little bit like how most waves can just pass right through each other without changing each other.

That being said, if magnetic fields are crazy intense, (say the magnetic fields near the surface of a magnetic pole of a neutron star) then there are some higher-order quantum effects that come into play.

This is due to the possibility that the photon splits into a virtual electron-positron pair and then recombines. An intense magnetic field could interact with the virtual pair and have an effect.

For instance, depending on how the virtual pair is aligned with the magnetic field, the energy level would be higher or lower, and this has an effect on how much of a contribution this possibility has.

This is called the Euler-Heisenberg interaction.

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In classical physics, electromagnetic fields and waves are additive so nothing can happen in vacuum between electromagnetic fields. They don't see each other.

In quantum physics, photons theoretically DO interact. The effect is rather small even in high-energy experiments, so don't expect some visible distortion with visible light and an iron magnet.

https://en.wikipedia.org/wiki/Two-photon_physics

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