Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 40

the magnetic D can be considered as perpendicular

to the path of the electric current, it therefore follows:

eld in the case of B CandA

- -

! ? !

d l d l

) ¼ 0 ð 3 : 7 Þ

eld equals zero (this will also be discussed
later in the text where we deal with static magnetic

Along the path CD the magnetic

elds, related to permanent
magnets). Therefore, only the path AB contributes to the magnetic eld:

Hl AB ¼ IN AB ð 3 : 8 Þ

where l AB represents the length of the path A B and N AB represents the number of

-

turns.
If the solenoid represents a torus-like shape (Fig. 3.2 c), it is called a toroid or
toroidal coil. All the magnetic

ux is held inside such a coil. In a toroid with the
number of turns N, the relation in Eq. ( 3.8 ) can be written as:

fl

IN
2 p r

H ¼ ð 3 : 9 Þ

where r is the radius of the toroid.
The electric current can be de ned by the current density, which passes a certain

area A as:

Z

! d !

¼ ð 3 : 10 Þ

I

A

Equation ( 3.6 ) can be written as:
I Z

! d l ! d ! ¼ ð 3 : 11 Þ

C ¼ C

A

where we consider the path Γ to be a closed eld-line C. By applying Stokes

theorem, Eq. ( 3.11 ) can be rewritten to obtain:
I Z

rot ! d ! ¼ ! d ! rot ! ¼ ! ) ð 3 : 12 Þ

A A

eld is a property of the space that surrounds an electric current
and a magnet, then the response of the material to the external magnetic

If the magnetic

eld is the

magnetic induction B (magnetic fl ux density). The relationship between the mag-

netic eld H and the magnetic induction B is actually related to the characteristics of

the material. In a vacuum, these characteristics follow the linear relation as: