Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 63

Fig. 3.22 A toroid with an
opened “ gap ”

For the case of the magnetic fl ux in the middle of the solenoid (z = 0), Eq. ( 3.88 )

will reduce to:

2
4

3
5

q

L

2 2

a 2

a 2 þ þ

l 0 IL
2 d 2

Ba ðÞ¼ ; 0 ln q

L

ð 3 : 89 Þ

2 2

a 1

a 1 þ þ

Now, if a soft magnetic permeable iron is placed inside such a gap, the magnetic

fl ux density B will be substantially increased as the sum of the magnetic eld and

the magnetization. Therefore, the iron will multiply the magnetic eld due to the

current. If we consider a simple iron toroid (Fig. 3.22 ) with the wires around it, then
the magnetic eld (internal magnetic eld) can be de ned by Eq. ( 3.9 ):

IN
2 p a ¼

IN
L

B ¼ ð 3 : 90 Þ

The magnetic fl ux density can then be considered as:

NI
L þ

¼ l 0 ð 3 : 91 Þ

B M

and:

L ¼

B
l 0 M

BL
l iron

NI ¼ ð 3 : 92 Þ

ux leakage occurs in
the air gap and we ignore the demagnetization effect, then it follows:

If we consider the air gap to be very small, so no magnetic fl