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Physics LibreTexts

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 \mu_o H = \mu_o nI. If we now place an iron rod of permeability \mu inside the solenoid, this doesn't change H, which remains nI. The B-field, however, is now B=\mu H. This is greater than \mu_oH, and we can write

B = \mu_o(H+M) \label{12.3.1}

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 \mu_o H = \mu_o nI, which is the externally imposed field, and the component \mu_oM, 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 = \mu_0H + M \nonumber

so that the magnetization would be the excess of B over \mu_0H. The equation B = \mu_0H + M, would be analogous to the familiar

D= \epsilon_oE + P \nonumber

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 = \mu_o (H+M). \nonumber

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 \chi_m of the material:

M = \chi_m H. \label{12.3.2}

On combining this with Equation \ref{12.3.1} and B = mH, we readily see that the magnetic susceptibility (which is dimensionless) is related to the relative permeability \mu_r = \mu/\mu_o by

\mu_r = 1+ \chi_m \label{12.3.3}


This page titled 12.3: Magnetization and Susceptibility is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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