Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 46

3.1.5 External, Internal Magnetic Field
and the Demagnetization

Note also that Eq. ( 3.36 ) does not correspond only to the creation of the magnetic

eld H by conduction currents. Namely, in magnetic materials, the eld will be

produced around it as well as within its volume [ 13 ]. Therefore:

H

¼ H c þ H m ð 3 : 37 Þ

The H c represents the eld created by conduction currents and H m is the mag-

netic eld due to the magnetization distribution of other magnetic eld sources or

the magnet itself. H m can be denoted as the demagnetization eld (stray eld

outside a magnet). Namely, the magnet creates “ free poles ” on the surface of the

material that creates the demagnetization eld H dem , which acts in an opposite

direction to magnetization M inside the magnet. The magnetic eld also acts in a

different direction than the magnetic ux density B. Figure 3.6 shows the case of the

uniformly magnetized material with no external magnetic

fl

eld sources. The mag-

netic eld H can be named as the internal eld H in , and the H c relates to the external

magnetic eld H out , which is produced by steady electric currents or the stray eld

outside the sample volume. H out is also named the applied eld. Therefore, it can be

written as [ 13 ]:

H in ¼ H out þ H d

ð 3 : 38 Þ

The demagnetization eld H dem is related to the magnetization M as:

H dem ¼

N dem M ð 3 : 39 Þ

where N dem represents the demagnetization factor — a tensor that is usually repre-

sented by a symmetric 3 × 3 matrix and is dependent on the geometry of the

Fig. 3.6 Magnetic eld outside and inside a bar magnet, magnetization inside the bar magnet and
magnetic eld induction (magnetic fl ux density inside and outside the magnet) and their relation