Annealed low-carbon iron has a susceptibility of order
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetic materials · Magnetic materials
The Boundary-Value Problem, Ch Magnetisation, bound currents and H, completed
Problem
Annealed low-carbon iron has a susceptibility of order χm=3000, a typical value quoted in magnetic-materials handbooks for soft iron in a small applied field. A sample is machined into a prolate ellipsoid of aspect ratio 5 (length to diameter), for which the demagnetising factor along the long axis is Na=0.0558 (quoted from the standard ellipsoidal-integral tables).
((a)) Calculate the apparent susceptibility χapp that a magnetometer would report for a field applied along the long axis.
((b)) Calculate the limiting apparent susceptibility 1/Na that any sample of this shape would report as χm→∞, and compare it with the answer to part (a).
((c)) State what this comparison shows about what such a measurement is actually sensitive to.