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Where, B_0 is the external field and B_m is the field inside a material.

Now, we get,

B = B_0 + μ_0*M (M is the magnetization)

My question is -

Do I always have to use μ_0 ? If yes then Why?

The material isn't free space, is it?

& also

B = μ_0*(H + M) , where H is the Magnetic Field Intensity/Strength

Same problem here. Do I always have to use μ_0 here too? Why not only μ ??

The main problem is we know Magnetic Field inside a material is B_m = μ_0*M

Why we are using μ_0 here while the material isn't free space!?

This problem is the main reason of those 2 questions I asked before.

Please help..