What would happen to the magnetic fields of a solenoid if it were wrapped around a hollow ferromagnetic core?
The magnetic field would be concentrated in the areas occupied by the mass of the ferromagnetic core. The empty centre of the core would be largely devoid of magnetic lines of flux. This usually means that there will be a higher level of flux density in the material mass of the core compared to a solid core.
However, at the ends of the core (where air dominates), the flux lines would rapidly become very similar the those lines of a solid ferromagnetic core.