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When an electrical current flows through a conductor and produces a magnetic field, does the magnetic field in the conductor form at the drift speed of the electrons in its structure or the velocity factor of the current?

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The model of a magnetic field induced by current that one generally sees in a textbook is based on an equilibrium, steady-state condition. In a dynamic situation, the magnetic field will be more complicated. Once one part of the wire has current flowing through it, all of the wire can have some magnetic field around it; the magnetic field doesn't stay just where there is current, but flows out into space. If there isn't anything to stop it, the magnetic field will expand at $c$. So if the current is moving slower than $c$, some of the magnetic field will overtake it.

However, the magnetic field attenuates as it expands, decreasing with the square of the distance. The normal formula you see in a textbook, with the field strength being inversely proportional to the distance, rather than the square, comes from a model of the wire being infinitely long, and the magnetic field from parts of the wire next to a particular point reinforcing the magnetic field from that point.

So to reach that level of magnetic field, the electric field has to had flowed to that part of the wire. It's the current, not any particular charges, that causes the magnetic field, so drift velocity is irrelevant.

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  • $\begingroup$ As it is the field of the current that causes it, then I imagine that the magnetic field originating within a material will move at the velocity factor, correct? $\endgroup$ Commented May 27, 2021 at 1:22

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