Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 49

B
H

l ¼ ð 3 : 48 Þ

Analogous to susceptibility, the magnetic permeability can be also expressed in
differential terms:

dB
dH

l 0 ¼ ð 3 : 49 Þ

Sometimes the term relative permeability is applied. This represents the ratio
between the permeability of the material divided by the permeability of free space
(vacuum, see Eq. 3.14 ):

l
l 0

l r ¼ ð 3 : 50 Þ

It also follows:

l r ¼ v þ 1 ð 3 : 51 Þ

3.1.7 Magnetic Force and Torque on a Dipolar Material

Let us now consider a magnetic material (a soft or hard ferromagnet) that is under
an applied magnetic eld H out . The magnetization vector M is aligned along the

material, as shown in Fig. 3.9 . At each end of the material there exists poles p,
de

ned with the intensity of M as [ 12 ]:

p ¼ M A l 0 ¼ q A A ð 3 : 52 Þ

Fig. 3.9 The gradient
magnetic eld over the
magnetic material