Magnetic flux and inductance?

[Thomas_h_h_]

If a current flows in a straight wire, a certain amount of magnetic flux will be generated around it.

Now suppose I put an iron tube around the wire (but don't change the current). I know the inductance will increase, but is that because more total flux is now being generated, or is the total flux still the same but more of it is now concentrated in the iron, close to the wire, instead of floating around far away in the air as previously?

Putting it another way, I know the flux density close to the wire will increase, but it that because more actual flux is generated or is it because some of the flux in the air has been 'sucked up' into the iron instead (so the flux density in the air has been reduced -a trade from one place to the other)?

 

[NFuller]

The magnetic field is concentrated in the iron because of the higher magnetic permeability of iron.

 

[Thomas_h_h_]

Yes but that doesn't answer my question though

 

[cnh1995]

From Ampere's law around the wire,
∫H.dl=I, where I is the current in the wire.
Since you used a circular iron tube, H will be constant on its circumference and ∫dl=2πr.
So,
H=I/2πr.
But flux density B=μH.
So, in the iron tube, the flux density will be more than it would be without the iron tube, which means more actual flux is produced.

 

[Thomas_h_h_]

So the H field remains unchanged in the air outside the tube?

 

[cnh1995]

So the H field remains unchanged in the air outside the tube?

Yes.