Magnetic field around a wire near ferrous materials

[EddieP]

I was wondering if I could ask a question on the magnetic field surrounding a current-carrying wire, and how this field might change with the presence of other, ferrous materials nearby.

I have been using this web page
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c3
to calculate the magnetic field around the wire, which the page shows moving in concentric circles.
The site gives the formula B = (μ0*I)/(2*pi*r) Where I is the current in Amperes, and r is the distance from the wire in meters.
This formula is for a wire surrounded by air, but I am wondering what might happen if some other objects were close to the wire (as close as r in the formula)

I am interested in a situation where a high permeability object and a low permeability object are positioned equal distance from the wire.
I am assuming the presence of the high permeability material would make the magnetic field around the wire stronger.
Would the field would still flow in a concentric circle, or would the field be diverted in the direction of the high permeability material?
If the goal was to exert a stronger force on the low permeability object, would the resulting magnetic field have a stronger effect on the low permeability object?

 

[Hesch]

I am wondering what might happen if some other objects were close to the wire

The magnetic field will be distorted. Think of if you have to travel some ( long ) distance by car, you will prefer to use the highway for a long distance, though the total distance ( distance on highway + distance on smaller roads ) may become some longer. You are choosing the fastest way, not the shortest.

The material with the high permeability is the highway, air is the smaller road.

 

[Hesch]

If the goal was to exert a stronger force on the low permeability object, would the resulting magnetic field have a stronger effect on the low permeability object?

Yes, because the path through the air has been shortened a bit, thus the field strength of the magnetic field, measured in the unit [ A/m ], has increased outside the object with high permeability, and thus at the location of the low permeability object. ( I don't know if that is understandable? ).