What is the magnetic field produced due to a current passing through a conductor?
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An electric current (a flow of electric charge) has an associated magnetic field regardless of the material (or space) the flow occurs in. This is a fundamental part of electromagnetism, rooted in observation, and quantified in Ampere's Law.
I which to emphasize that this phenomenon is considered to be fundamental in nature, which means, there cannot be a "more" fundamental explanation (for, if there were, electromagnetism would not be fundamental).
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