12.3: Magnetization and Susceptibility
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The H-field inside a long solenoid is nI. If there is a vacuum inside the solenoid, the B-field is μoH=μonI. If we now place an iron rod of permeability μ inside the solenoid, this doesn't change H, which remains nI. The B-field, however, is now B=μH. This is greater than μoH, and we can write
B=μo(H+M)
The quantity M is called the magnetization of the material. In SI units it is expressed in A m-1. We see that there are two components to B. There is the μoH=μonI, which is the externally imposed field, and the component μoM, originating as a result of something that has happened within the material.
It might have occurred to you that you would have preferred to define the magnetization from
B=μ0H+M
so that the magnetization would be the excess of B over μ0H. The equation B=μ0H+M, would be analogous to the familiar
D=ϵoE+P
and the magnetization would then be expressed in tesla rather than in A m-1. This viewpoint does indeed have much to commend it, but so does
B=μo(H+M).
The latter is the recommended definition in the SI approach, and that is what we shall use here.
The ratio of the magnetization M ("the result") to H ("the cause"), which is obviously a measure of how susceptible the material is to becoming magnetized, is called the magnetic susceptibility χm of the material:
M=χmH.
On combining this with Equation ??? and B=mH, we readily see that the magnetic susceptibility (which is dimensionless) is related to the relative permeability μr=μ/μo by
μr=1+χm