Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 39

Now, let us consider Ampere ' s law [ 7 ], which states that the magnetic eld

intensity, measured at a distance r from current I, is proportional to:

/

!

I
r

ð 3 : 4 Þ

For a circular conduit with the closed path Γ , and with radius r, Eq. ( 3.3 ) can also

be written as:

H ðÞ/ 2 p r I ð 3 : 5 Þ

The magnetic eld that is generated in this case can be expressed using

Ampere ' s law as:

I

!

d l ¼ I ð 3 : 6 Þ

C

For any closed-loop path, the closed line integral of the magnetic eld is equal to

the electric current encircled by such a loop.
Figure 3.2 a shows a coiled wire wound in several turns (a solenoid) in which the
circulating current produces an almost uniform magnetic

eld. In such a case the

magnetic eld can also be treated as being parallel with the coil axis (Fig. 3.2 b). For

this particular case we will consider the path given by A B C D in Fig. 3.2 b. Since

- - -

Fig. 3.2 a The current-eld relation in a coil and, b a uniform solenoid, where Ampere ' s law is

applied to the rectangular path A B C

-

D A, c a uniform toroid