Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 52

Fig. 3.11 A simple
permanent-magnet assembly
consisting of a magnet and
soft iron with the air gap

H mag L mag þ H gap L gap ¼ 0 ð 3 : 60 Þ

Because there is no magnetization in the air gap, the magnetic fl ux density in the

air gap can be simply written as (see Eq. 3.36 ):

B gap ¼ l 0 H gap ð 3 : 61 Þ

By rearranging Eqs. ( 3.59 ) ( 3.61 ) we obtain [ 14 ]:

-

B mag
l 0 H mag ¼

A gap L mag
A mag L gap

ð 3 : 62 Þ

By using Eqs. ( 3.59 ) ( 3.61 ) we can also obtain:

-

B 2
gap

V gap
l 0

B mag H mag V mag ¼ ð 3 : 63 Þ

where V mag ,V gap represent the volume of the magnet and the air gap, respectively.
The maximum magnetic ux density in the air gap will be achieved with the

product B mag H mag being a maximum (BH) max . This is why this product also rep-
resents a

fl

gure of merit for permanent magnets.
The working point of a permanent magnet is de ned by the intersection of the

load line and the BH loop (Fig. 3.12 ). The maximum (BH) max point for an isolated
magnet with an ideal square magnetization loop (Fig. 3.12 ) can be calculated by
maximizing the product of ʼ 0 (H mag +M) H mag . This depends further on the shape of

the magnet, and the demagnetization factor N dem :