Demagnetization factors for ellipsoids
Practically useful magnetic materials usually possess a spontaneous magnetization (ferromagnets) or give a large response to magnetic field. For the purpose of precise measurements, it is good to perform a careful analysis of the demagnetization factors, as in such circumstances, the sample shape contributes nontrivially to the effective field acting on the sample.
If H is the external field (in SI units, i.e. in T), and N the demagnetization factor (dependent only on the sample shape), the effective field Heff acting on the sample depends on the sample magnetization M(H) (in A/m units) as:
Heff = H – N M(Heff).
In the CGS units (field in Oe, magnetization in emu) this formula reads:
Heff = H – 4 π N M(Heff).
Demagnetization factors for cylinders (column 2, Nm(0)) and ellipsoids (column 4, N) with semiaxes a, b (with a = b) and c (here column 1 is γ = c / a) can be calculated exactly and are listed in the following table.
