Confusing on permeability and relative permeability

[KFC]

In some textbook of fundamental electromagnetism, the relation between magnetic field $$\vec{B}$$ and so called magnetizing field $$\vec{H}$$ is

$$\vec{B} = \mu_0\vec{H}$$

But later on, they introduce a so called relative permeability

$$\mu_r = \frac{\mu}{\mu_0}$$

I might be wrong but my understanding of this definition is relative permeability is used to tell the 'capability to affect the field' of the object while comparing to something in free space? So $$\mu$$ is actually the total and absolute permeability of that object?

And I am quite confusing with $$\vec{H}$$ here. Now then we have the $$\vec{B}$$ to describe the magnetic field, why we need another field variable? Someone said it may related to magnetization. But if there is a magnetization so

$$\vec{B} = \mu_0(\vec{H} + \vec{M}) = \mu_0\vec{H}$$

why we still have to use H ?

My last question is: if a material with relative permeability $$\mu_r=\mu / \mu_0$$ is considered, the relation between B and H will modified to

$$\vec{B} = \mu_r\vec{H}$$

or

$$\vec{B}=\mu\vec{H}$$

or

unchanged?

Thanks

 

[adriank]

Often, H is much more easily controlled, so H is much more useful both for practical purposes and in calculations. In fact, quite often H is introduced before B.

H behaves much more nicely in the presence of matter, where the magnetization is not in general zero. It's a similar relationship between E and D, but in practice it is E that is more easily controlled.

In linear media, B = μH. The relative permeability μ_r is dimensionless, so the dimensions wouldn't work out if you used that instead.

The magnetic susceptibility χ_m (which is dimensionless) determines the magnetization in (linear) matter: M = χ_mH. Thus B = μ₀(H + M) = μ₀(1 + χ_m)H = μH, where μ is defined to be μ₀(1 + χ_m). And then μ_r = μ / μ₀ = 1 + χ_m.

 

[KFC]

Thank you so much. In your reply, you said: In linear media, B = μH ... I wonder if μ here is the total permeability? That is, μ=μ_r*μ₀ ?

Often, H is much more easily controlled, so H is much more useful both for practical purposes and in calculations. In fact, quite often H is introduced before B.

H behaves much more nicely in the presence of matter, where the magnetization is not in general zero. It's a similar relationship between E and D, but in practice it is E that is more easily controlled.

In linear media, B = μH. The relative permeability μ_r is dimensionless, so the dimensions wouldn't work out if you used that instead.

The magnetic susceptibility χ_m (which is dimensionless) determines the magnetization in (linear) matter: M = χ_mH. Thus B = μ₀(H + M) = μ₀(1 + χ_m)H = μH, where μ is defined to be μ₀(1 + χ_m). And then μ_r = μ / μ₀ = 1 + χ_m.

 

[adriank]

By μ I mean exactly μ, the permeability of the material.