Question

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)`?

Answer 1

You are correct.

We should use `mu(=mu_0mu_r)` 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~~1.0`

Hope this helps.