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*