Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 45

I

dA

J m

¼ 0 ð 3 : 29 Þ

A

If we express the magnetization current as the rotor (curl) of the magnetization
vector, then it follows by Stokes theorem:
I

I

! rot ! d ! d ~ s ¼ ð 3 : 30 Þ

C A

If the path lies entirely outside the magnetized body it follows for any surface
[ 13 ]:

I

rot ! d ! ¼

0 ð 3 : 31 Þ

A

with [ 10 , 13 ]:

! ¼

M

J m rot ð 3 : 32 Þ

Following Eq. ( 3.12 ), the conducting current density equals:

J ! ¼

rot H ð 3 : 33 Þ

By following Eq. ( 3.32 ), this can be now expressed as:

rot ! ¼ l 0 rot H þ

rot M ð 3 : 34 Þ

From Eqs. ( 3.16 ) and ( 3.34 ) it follows:

r H ¼r M ð 3 : 35 Þ

We can also de ne the following general relation.

B

¼ l 0 H þ M

ð 3 : 36 Þ

This is known as the Sommerfeld convention. Equation ( 3.36 ) will reduce to
Eq. ( 3.13 ) in the case of a vacuum with M =0.