Magnetic field from a conductor surrounded ~350 deg by iron?

If a conducting wire with an applied current is surrounded by a sleeve of iron or similar with a channel cut in one side so that there is an air gap running along the length - would this

A) concentrate the field radiated from the wire to the open side - (instead of radiating in 360 deg it would be restricted to say 10 deg)?

B) amplify the field due to the conductor as a magnetic core does when placed inside a coil (as stated in the Wikipedia page on Magnetic_core 'The use of a magnetic core can increase the strength of magnetic field in an electromagnetic coil by a factor of several hundred times what it would be without the core')?

How would I go about calculating the field strength and direction? Is this configuration commonly used for anything / have a name I can search for?

I'm looking for ways to increase the flux density in specific regions for a motor without using permanent magnets

• If you are considering the magnetic field, why does it matter if the center wire is conducting? – Al Nejati Sep 13 '18 at 1:24
• I'm considering the field generated by the conducting wire. – user263399 Sep 13 '18 at 3:15

The presence of an air gap has a dramatic effect on the configuration of the field lines.

Without the air gap (a continuous shield of magnetic material), most of the field lines rotating around the wire would be inside the magnetic material.

With the addition of an air gap, even a small one, you get a phenomenon known as flux fringing. The flux becomes far less concentrated in the entirety of the magnetic material, and 'spills out' in the vicinity of the air gap.

Versus the situation where you have no magnetic material at all, the magnetic flux in the air gapped material is much higher. However it is still far smaller than the magnetic field you would find in the material, without an air gap, assuming current through the conductor is constant.

To put it another way, with an air gap you need far more current through the conductor to achieve the saturation field level of the magnetic material.