Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 48

Fig. 3.8 Demagnetization eld in ellipsoids. The value of the demagnetization eld H dem will be
higher in the case when the poles are closer to each other (right case), and smaller when they are
distant (left case)

B in ¼ l 0 M 1

ð N dem Þ ð 3 : 44 Þ

eld, the N dem should limit to zero.
This is the case when the material is thin, very long and magnetized along its major
axis. In Fig. 3.8 , two ellipsoids are shown. Along the principal axes of the ellipsoid,
H dem and M will be collinear. In the

In order to have the smallest demagnetization

rst case the demagnetization factor, due to

distant “ free poles ” , will be smaller than in the case when the “ free poles ” are closer.

3.1.6 Magnetic Susceptibility and Permeability

In order to de ne the response of a material to an applied magnetic eld, a

dimensionless property, the susceptibility, can be de ned as:

M
H

v ¼ ð 3 : 45 Þ

Since the magnetization is not always a linear function of the magnetic eld

(internal magnetic eld), the susceptibility or the magnetic permeability are also not

constants. The susceptibility may also be expressed in a differential way:

dM
dH

v 0 ¼

ð 3 : 46 Þ

Note also that the external susceptibility can be de ned. In this particular case,

instead of the internal, the external (applied magnetic eld) is used:

M
H out

v out ¼ ð 3 : 47 Þ

The magnetic permeability de nes the ratio between the magnetic fl ux density

and the internal magnetic eld.