It is possible to express the magnetic susceptibility xm in several different units. For the discussion of this chapter, xm was used to designate the volume susceptibility in SI units, that is, the quantity that gives the magnetization per unit volume (m3) of material when multiplied by H. The mass susceptibility xm (kg) yields the magnetic moment (or magnetization) per kilogram of material when multiplied by H; similarly, the atomic susceptibility xm (a) gives the magnetization per kilogrammole. The last two quantities are related to xm through the relationships
xm = xm (kg) × mass density (in kg/m3)
xm (a) = xm (kg) × atomic weight (in kg)
When using the cgs–emu system, comparable parameters exist, which may be designated by x’m, x’m(g), and x’m (a); the xm and x’m are related in accordance with Table 18.1. From Table 18.2, xm for silver is –2.38 × 10−5; convert this value into the other five susceptibilities.
Table 18.1 Magnetic Units and Conversion Factors for the SI and cgs–emu Systems
Quantity | Symbol | Derived | Primary | cgs–emu Unit | Conversion |
Magnetic induction (flux density) | B | tesla (Wb/m2)a | kg/s C | Gauss | 1 Wb/m2 = 104 gauss |
Magnetic field strength | H | amp-turn/m | C/m s | Oersted | amp-turn/m = 4π × 10–3 oersted |
Magnetization | M (SI) I (cgs–emu) | amp-turn/m | C/m s | maxwell/cm2 | 1 amp-turn/m = 10–3 maxwell/cm2 |
Permeability of a vacuum | µ0 | henry/mb | kg m/C2 | Unitless (emu) | 4π × 10–7 henry/m = 1 emu |
Relative permeability | µr (SI) µ' (cgs–emu) | Unitless | Unitless | Unitless | µr = µ' |
Susceptibility | xm (SI) x'm (cgs–emu) | Unitless | Unitless | Unitless | xm = 4πx'm |
Table 18.2 Room-Temperature Magnetic Susceptibilities for Diamagnetic and Paramagnetic Materials
Diamagnetics | Paramagnetics | ||
Material | Susceptibility xm (volume) (SI units) | Material | Susceptibility xm (volume) (SI units) |
Aluminum oxide | –1.81 × 10–5 | Aluminum | 2.07 × 10–5 |
Copper | –0.96 × 10–5 | Chromium | 3.13 × 10–4 |
Gold | –3.44 × 10–5 | Chromium chloride | 1.51 × 10–3 |
Mercury | –2.85 × 10–5 | Manganese sulfate | 3.70 × 10–3 |
Silicon | –0.41 × 10–5 | Molybdenum | 1.19 × 10–4 |
Silver | –2.38 × 10–5 | Sodium | 8.48 × 10–6 |
Sodium chloride | –1.41 × 10–5 | Titanium | 1.81 × 10–4 |
Zinc | –1.56 × 10–5 | Zirconium | 1.09 × 10–4 |
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