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, $H$,

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

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

$$\mu = \frac{B}{H}$$ (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.

$$\chi \mu$$ Material/Ordering

$$=1$$

$$\lesssim 1$$

$$\gtrsim 1$$

$$\gtrsim 1$$

$$\gg 1$$

$$\gg 1$$