Magnetic field with and without ferrite core

[M.Kalai vanan]

An air core circular coil of n turns produced a magnetic field of (for eg) 0.5 tesla at a point in space (not within the coil nor along the axis of coil). If a ferrite core of μr (relative permeability)=200 and of the same length of the coil is inserted into the coil what happens to the magnetic field at the same point.
Will it increase by μr times or stay constant?
NOTE:
The magnetic field at the center of coil increases by μr times.

 

[Noctisdark]

The Magnetic Field will surely increase big times

β = μ0×I×n/(2πι) if the Coil is air core
However
β = μr×I×n/(2πι)
Where l is the distance to the coil ^^"
Hope I've helped ...

 

[Cruikshank]

My first instinct is to say, "all those extra field lines inside the coil have to go *somewhere*, so yes it increases, and by the same multiplier. That still sounds right after a minute of reflection. I've never learned any formulas for ferromagnetism, though.