Magnetic field of iron core solenoid

[foru0707]

When we calculate magnetic field of iron core solenoid, should we multiply "relative permeability" or "effective permeability"?

I thought that we should use relative permeability, but wiki(http://en.wikipedia.org/wiki/Solenoid) says that we should use effective permeability.

I'm so confused...
please help me.

 

[CWatters]

Permeability μ₀ - air/no core

L = k * μ₀ * N² * A/l

Relative Permeability μ_r - factors in the core material

L = k * μ₀ μ_r * N² * A/l

Effective permeability μ_e - Similar to μ_r but takes into acount factors such as air gaps, the shape of the core, winding layout. The effective permeability also changes if the core is saturated or fast pulses/high frequencies are involved.

L = k * μ₀ μ_e * N² * A/l