Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 43

Fig. 3.5 The torque on a
electric circular loop carrying
a current I and placed in a
uniform magnetic eld

T

F 4 ¼ cos u i sin u k IaBk cos u IB j ¼~ r b þ b ¼ ab ð 3 : 20 Þ

T ¼ IB ab cos u ð 3 : 21 Þ

where φ is the angle of inclination of the coil ' s plane, and the A ¼ a b represents

the area surrounded by the coil.
The surface A can be represented by the vector:

A

¼ A ~ n ð 3 : 22 Þ

where n stands for the unit vector normal to the surface A. Now the torque, written

as the vector, is:

~

T

I A l 0 H ¼ ð 3 : 23 Þ

The area A (which constitutes the complete loop) is coincident with current I.
The product of the two is de ned as the magnetic dipole moment, which is con-

sidered to be the elementary magnetic quantity:

I A

m m ¼ ~ ð 3 : 24 Þ

3.1.3 Magnetization

The magnetic moment ~ m m per unit volume of a solid can be de ned as the

magnetization: