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Does magnetic flux surround a *ferrous* conductor?

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Circlotron:
Normally when you pass a current down a copper wire, the magnetic field rotates around the axis of the wire. Imagine if you passed this same current down the length of a steel rod. Would the field surround the rod or would it be contained completely within the rod seeing it is ferrous and therefore has much lower reluctance than the surrounding air. If it does stay inside it, does that mean there would be no mutual induction between our steel conductor and another (say, copper) conductor running parallel to it?

ejeffrey:
No there will still be the same magnetic field outside the conductor given by Ampere's law.

thinkfat:

--- Quote from: ejeffrey on June 30, 2019, 02:27:15 pm ---No there will still be the same magnetic field outside the conductor given by Ampere's law.

--- End quote ---
You sure? That law is a simplification for one-dimensional conductors, isn't it?

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ejeffrey:
Definitely sure.  Ampere's law is always valid.  There are many special cases for specific geometries you can derive from the general law, but it it one of the fundamental laws of classical electromagnetism.

You also can't screen a long straight wire carrying a DC current with a ferrous material surrounding the wire.  The only way to screen a current carrying wire is to have an equal and opposite current flowing through the screen as is ideally done in coaxial cables.

The place magnetic shielding comes in is when you already have no net current flow.  For instance, a circular loop with a current through it or a solenoid.  In that case, the ferrous material provides a path of low reluctance to complete the flux rings created by the loop. 

If you have a pair of wires carrying opposite currents (a balanced line), the net current is zero and thus the total magnetic field around a loop containing both wires is zero.  However, the local field can be non zero depending on which wire is closer.  A magnetic shield containing both wires will reduce the external magnetic field in this case.

cur8xgo:

--- Quote from: Circlotron on June 30, 2019, 12:46:28 pm ---Normally when you pass a current down a copper wire, the magnetic field rotates around the axis of the wire. Imagine if you passed this same current down the length of a steel rod. Would the field surround the rod or would it be contained completely within the rod seeing it is ferrous and therefore has much lower reluctance than the surrounding air. If it does stay inside it, does that mean there would be no mutual induction between our steel conductor and another (say, copper) conductor running parallel to it?

--- End quote ---

I'm going to say that the field outside the conductor doesn't change at all whether or not the conductor is steel or copper, assuming the same current flows in either case.

The field inside the conductor will of course be vastly different if the conductor has a vastly different permeability between the two cases.

An electric analogy would be a circuit composed of a 1 billion ohm resistor (air/copper) in parallel with a 1 ohm resistor (steel). The current (magnetic flux) through the 1 billion ohm resistor doesn't change at all regardless of whether the 1 ohm resistor is present or not.

This assumes DC current flow, no other currents nearby, infinitely long straight wire...

Edit: deleted hand wavy sloppy thinking about mutual induction

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