Two ways to look at it.
1 – The electric and magnetic forces are unified. James Maxwell wrote down some equations stating exactly this. From this point of view, the fact that moving electric fields create magnetic fields is a fundamental feature of the universe, rather than something to be explained by using other laws.
2 – Special relativity can also be used as an explanation. An easier way to explain this is with [this 5 minute video](https://www.youtube.com/watch?v=1TKSfAkWWN0).
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