Does Every Iron Core Have the Same Relative Permeability?

[Dash-IQ]

B = μ₀nI
Usually, the value of B is quite small...
I'd like to boost the magnetic field B to a much larger and stronger field, and the most efficient way I find to do that is using a high permeability core B = ku₀nI.
What is the average μ_r of an iron core? They range from what value?
Do all iron have the same relative permeability?

 

[Dash-IQ]

+ With the use of a high permeability ferromagnetic cores, it makes it more practical for electromagnets to have a magnetic field a Tesla and possibly higher?

 

[Meir Achuz]

For most iron, mu changes drastically with I.
It also depends on what you want the core to do. For an electromagnet or transformer you want B to go back to zero elastically when I goes to zero. For more permanent magnetism, you want a fat hysteresis loop.

 

[Dash-IQ]

For most iron, mu changes drastically with I.

Can you elaborate please on that(i.e example with values)?
Are u_r of ferromagnets based on I? or are they a constant value when I = 0 or I = x Amps?
Is it true that their u_r are over a 1000?

The rest I'm quite familiar with, as you are describing soft core(e.g iron low coercivity), and hard core's that are best when creating permanent magnets with(e.g neodymium low coercivity wider hysteresis area).