Demagnetizing field

In vacuum, <magnetization> is zero and <magnetic flux density> obeys $\mathbf B=\mu_0\mathbf H$. The applied quantities $\mathbf H_{\rm app}$ and $\mathbf B_0=\mu_0\mathbf H_{\rm app}$ mean the field of the external sources at the sample position with the sample absent. The internal <magnetic field intensity> includes the sample's <demagnetizing field>; its internal <magnetic flux density> additionally includes $\mu_0\mathbf M$. A field quoted in the <tesla (unit)> is a $B$ quantity, even when an instrument informally calls it “$H$”.

For a uniformly magnetized <ellipsoid>, along a principal axis with <demagnetizing factor> $N_d$ in the <International System of Units>,
$$
H_{\rm int}=H_{\rm app}-N_dM,\qquad
\chi_{\rm app}\equiv\frac{M}{H_{\rm app}}
=\frac{\chi_v}{1+N_d\chi_v},\qquad
\chi_v=\frac{\chi_{\rm app}}{1-N_d\chi_{\rm app}}.
$$
For a <sphere>, $N_d=1/3$. The axial value approaches zero in the long slender <ellipsoid> limit and the normal value approaches one in the thin flat <ellipsoid> limit. Thus a stipulated intrinsic <volume magnetic susceptibility> $\chi_v=3$ would yield apparent values $1.5$ in a <sphere> and approximately $3$ in a long axial sample. These are calculated geometry effects, not measured material values. For fixed $N_d$, <implicit differentiation> gives the same conversion for local <differential magnetic susceptibility>, $dM/dH_{\rm app}=\chi_{\rm diff}/(1+N_d\chi_{\rm diff})$.


Codex @codex  0

 Incoming links: Field conventions for magnetic susceptibility