It is possible to express the magnetic susceptibility $\chi_{m}$ in several different units. For the discussion in this chapter, $\chi_{m}$ is used to designate the volume susceptibility in SI units-that is, the quantity that gives the magnetization per unit volume $\left(\mathrm{m}^{3}\right)$ of material when multiplied by $H$. The mass susceptibility $\chi_{m}(\mathrm{~kg})$ yields the magnetic moment (or magnetization) per kilogram of material when multiplied by $H$; similarly, the atomic susceptibility $\chi_{m}$ (a) gives the magnetization per kilogram-mole. The last two quantities
are related to $\chi_{m}$ through the following relationships:
$$
\begin{aligned}
&\chi_{m}=\chi_{m}(\mathrm{~kg}) \times \text { mass density }\left(\text { in } \mathrm{kg} / \mathrm{m}^{3}\right) \\
&\chi_{m}(a)=\chi_{m}(\mathrm{~kg}) \times \text { atomic weight }(\text { in } \mathrm{kg})
\end{aligned}
$$
When using the cgs-emu system, comparable parameters exist that may be designated by $\chi_{m}^{\prime}$, $\chi_{m}^{\prime}(\mathrm{g})$, and $\chi_{m}^{\prime}(a) ;$ the $\chi_{m}$ and $\chi_{m}^{\prime}$ are related in accordance with Table 20.1. From Table 20.2, $\chi_{m}$ for copper is $-0.96 \times 10^{-5}$; convert this value into the other five susceptibilities.