Field outside a ferrite cored coil

[EMRF]

The field outside a coil is given by

I notice permeability of vacuum in the expression, and this makes sense since we are evaluating the field in space.
Is there any effect to the coil having a ferrite core? Looks like there should not be (again the field is evaluated in space).
However, looking at a two coil communication system the mutual inductance is proportional to BOTH inductance values , primary and secondary , and the coupling factor. So it would seem the field at the secondary coil location is at least partially influenced by the primary coil's inductance which is proportional to the ferrite permeability.

 

[gtoguy97]

If so, how would I show that in the expression ? I'm not sure if this is correct. The field outside a coil is determined by the current flowing through the coil, and is not influenced by the permeability of any material surrounding the coil. The magnetic field around a coil of wire can be determined using Ampere's law. The permeability of the medium will affect the magnetic field within the coil, but not the field outside.