# Why we use mu_0 for air when calculating the magnetic flux density inside an electric cable where (r<R) instead of the permeability of the metal core mu. " " B=(mu_0Ir)/(2piR^2)?

We should use $\mu \left(= {\mu}_{0} {\mu}_{r}\right)$ in the formula.
Having said we also observe that most non-ferromagnetic substances (such as wood, plastic, glass, bone, copper, aluminum, air and water) have a permeability almost equal to μ_0, as their relative permeability ${\mu}_{r} \approx 1.0$