Does magnetic flux surround a *ferrous* conductor?

[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]

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

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

Gesendet von meinem Nokia 6.1 mit Tapatalk

[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]

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?

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

[T3sl4co1l]

You're working kind of backwards -- the external field is the same; the internal field is more intense.

Which, since the field within the conductor opposes flow of current in the conductor -- this causes the field to decay extremely quickly under the surface of the conductor.

That is to say, this is precisely why skin effect is so much more exaggerated for magnetic conductors.

Tim

[L_Euler]

Ampere’s law does not include a term for material or material properties. The field will be the same for all materials

[Zero999]

One hint: many coax cables are made from steel cores.

Why? Surely the skin depth at those frequencies with a ferrous conductor would be so tiny, the losses would be huge, or does steel stop being magnetic at high frequencies?

[Rerouter]

How thin is that plating that it makes it worthwhile over straight copper?? Silver is like $450 per kg, Copper plated steel does exist...

[T3sl4co1l]

It's copper and/or silver platings, the combination and thickness depends on the wire grade.  You do indeed see the added losses at low frequencies, but at RF it's fine.

A related matter is plating of waveguides.  Normally you'd use steel base (cheap, strong), then copper, nickel and silver (copper for bonding, nickel for diffusion barrier to prevent spontaneous alloying, silver for the intended surface), but if you order this from a plating shop without special instructions you'll find the nickel layer dominates and losses are shite.  The silver has to be extra thick, several skin depths, to be worthwhile.

Tim