Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-18 GTBL042-Callister-v2 September 17, 2007 17:37

Revised Pages

726 • Chapter 18 / Magnetic Properties

Table 18.1 Magnetic Units and Conversion Factors for the SI and cgs–emu Systems

SI Units

Quantity Symbol Derived Primary cgs–emu Unit Conversion

Magnetic

induction (flux

density)

B tesla (Wb/m^2 )a kg/s-C gauss 1 Wb/m^2 = 104 gauss

Magnetic field

strength

H amp-turn/m C/m-s oersted 1 amp-turn/m=

4 π× 10 −^3 oersted

Magnetization M(SI)

I(cgs–emu)

amp-turn/m C/m-s maxwell/cm^2 1 amp-turn/m=

10 −^3 maxwell/cm^2

Permeability of a

vacuum

μ 0 henry/mb kg-m/C^2 Unitless (emu) 4 π× 10 −^7 henry/m=

1 emu

Relative

permeability

μr(SI)

μ′(cgs–emu)

Unitless Unitless Unitless μr=μ′

Susceptibility χm(SI)

χ′m(cgs–emu)

Unitless Unitless Unitless χm= 4 πχ′m

aUnits of the weber (Wb) are volt-seconds.

bUnits of the henry are webers per ampere.

magnetic andχmis called themagnetic susceptibility,which is unitless.^1 The magnetic suscep-

susceptibility tibility and the relative permeability are related as follows:

χm=μr− 1 (18.7)

Relationship

between magnetic

susceptibility and

relative permeability There is a dielectric analogue for each of the foregoing magnetic field parameters.

TheBandHfields are, respectively, analogous to the dielectric displacementD

and the electric fieldewhereas the permeabilityμparallels the permittivity(cf.

Equations 18.2 and 12.30). Furthermore, the magnetizationMand polarizationPare

correlates (Equations 18.5 and 12.31).

Magnetic units may be a source of confusion because there are really two sys-

tems in common use. The ones used thus far are SI [rationalizedMKS(meter-

kilogram-second)]; the others come from thecgs–emu(centimeter-gram-second-

electromagnetic unit) system. The units for both systems as well as the appropriate

conversion factors are contained in Table 18.1.

Origins of Magnetic Moments

The macroscopic magnetic properties of materials are a consequence ofmagnetic

momentsassociated with individual electrons. Some of these concepts are relatively

complex and involve some quantum-mechanical principles beyond the scope of this

discussion; consequently, simplifications have been made and some of the details

omitted. Each electron in an atom has magnetic moments that originate from two

sources. One is related to its orbital motion around the nucleus; being a moving

charge, an electron may be considered to be a small current loop, generating a very

small magnetic field, and having a magnetic moment along its axis of rotation, as

schematically illustrated in Figure 18.4a.

(^1) Thisχmis taken to be the volume susceptibility in SI units, which, when multiplied byH,
yields the magnetization per unit volume (cubic meter) of material. Other susceptibilities are
also possible; see Problem W18.2, which is found on the book’s Web site.