Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 61

Furthermore, the amount of current fl owing through is proportional to the

thickness of the cross-section:

N
L Idz 0 ¼

nIdz 0

¼ ð 3 : 81 Þ

dI

The magnetic eld at point P can now be de ned as:

l 0 a 2

2

dB ¼ dI ð 3 : 82 Þ

2

2 a 2

þ ð

z 0

Þ

z

By taking into account Eqs. ( 3.81 ) and ( 3.82 ), the integral over the whole length
of the solenoid will lead to the following magnetic fl ux density at the point P.

L
2

Z

l 0 nIa 2
2

dz

B ðÞ¼

3
2

2

a 2 þ ð z z 0 Þ

L
2

ð 3 : 83 Þ

2 3

L L

l 0 nI
2

z
z

2

z
z þ

2 þ

4 5

¼ q þ q

2 2

L
2

L
2

þ a 2 þ a 2

ux
density. Therefore, in practice the coil will consist of several layers (Fig. 3.20 )of
wires (or a layer of a run with a certain thickness, such as for instance in so-called
Bitter magnets, see Fig. 3.21 ).
By taking Eq. ( 3.82 ), we can rearrange it for this particular case. Now, we deal
with the 2D problem, by adding the length a as the variable, by taking values from
a 1 to a 2 .

A single layer of wire will, in practice, not provide suf cient magnetic fl

Fig. 3.20 The solenoid
comprising several layers of
turns