Magnetic Response

The response of a material to a magnetic field is quantified by two quantities: the susceptibility, $ \chi $, which is the variation of magnetisation, $ M$, with applied field, $ H$,

$\displaystyle \chi = \frac{M}{H}$ (3.3)

and the permeability, $ \mu $, the variation of magnetic induction, $ B=\mu_{0}(H+M)$, with applied field,

$\displaystyle \mu = \frac{B}{H}$ (3.4)

Permeability is often quoted relative to $ \mu_{0} = 4\pi \times 10^{-7}\ensuremath{\unskip\,\mathrm{\nicefrac[\mathrm]{H}{m}}}$, the permeability of a vacuum or (within a high degree of accuracy) air.

The susceptibility and permeability of a material depends upon its magnetic characteristics. Table 3.1 gives an indication of how they vary with the type of material and magnetic ordering (if any) it displays.

Table 3.1: Variation of susceptibility, $ \chi $, and permeability, $ \mu $, with material and magnetic ordering.
Material/Ordering $ \chi $ $ \mu $

0 $ =1$

Small and negative $ \lesssim 1$

Small and positive $ \gtrsim 1$

Small and positive $ \gtrsim 1$

Large and positive $ \gg 1$

Large and positive $ \gg 1$

Dr John Bland, 15/03/2003