Let N be the demagnetization tensor in the principal axis system of a prolate (a > b) ellipsoid of revolution uniformly magnetized along its symmetry axis.

(a) Explain why only N_zz need be calculated.
(b) Cut the ellipsoid into circular slices with thickness d_z and radius ρ as shown in the figure. The bevelled edge of each slice is perpendicular to the ellipsoid normal n̂ and has edge length dℓ = d_z/ sin θ. On the other hand, if dℓ points along the circumference on any slice,

be the eccentricity of the ellipsoid. Use Amp`ere’s theorem (Section 11.3) and the Biot-Savart result for the on-axis magnetic field of a current ring to show that

(c) Check the spherical limit.

2b M- 2a ds 1 0 dz de