= Solution
Changing shape changes the <demagnetizing field>, and hence the <magnetization> induced by the same applied <magnetic field intensity>. For a small linear sample in the ellipsoid approximation, the force magnitude scales with
$$
\chi_{\rm eff}=\frac{\mu-1}{1+N_d(\mu-1)}.
$$
For $\mu>1$, a more elongated body aligned with the field has smaller $N_d$ and a stronger response. A sphere has $N_d=1/3$, giving $\chi_{\rm eff}=3(\mu-1)/(\mu+2)$; a very thin plate with field normal to it has $N_d\to1$, giving $(\mu-1)/\mu$. Thus \b[an axially slender rod generally experiences a stronger attraction than a sphere or a transverse thin plate of the same material and volume], within the linear uniform-applied-field approximation.
The shape response is precisely why the $1/\mu$ factor in part (c) cannot apply universally to every small magnetic body. Orientation also matters through the appropriate principal <demagnetizing factor>; for general nonellipsoidal bodies the internal field is not uniform and a single scalar correction need not be exact.
Back to article page
