Ferromagnetism — Question 7

Question 7

The demagnetizing load can exceed a magnet switching threshold

Use an ideal rectangular M-H model with positive saturated magnetization Ms and intrinsic switching threshold -Hc. An ellipsoid has $H_{\mathrm{int}}=H_a-NM$. It is initially saturated along +x; then Ha is reduced to zero.

1. Find the internal field if the sample remains uniformly saturated, and derive the condition for avoiding reverse switching during removal of Ha.

2. For $M_s=6.0\times10^5$ A/m and $H_c=1.2\times10^5$ A/m, compare shapes with N=0.05 and N=1/3. State what cannot be inferred once the uniform state becomes unstable.

Question 7 - Solution

The demagnetizing load can exceed a magnet switching threshold

(a) Method and calculation

$$H_a=0,\ M=M_s\Rightarrow\boxed{H_{\mathrm{int}}=-NM_s}.$$$$H_{\mathrm{int}}>-H_c\Rightarrow\boxed{N<H_c/M_s}.$$

(b) Interpretation and further calculation

$$H_c/M_s=0.20:\quad N=0.05<0.20,\quad N=1/3>0.20.$$$$\boxed{\text{The elongated sample passes; the sphere fails the uniform-state test.}}$$

Physical check

Failure predicts instability of the assumed saturated state, not its final domain pattern or final remanent moment.