10. Fields Due to Magnetized Dipoles

10. FIELDS DUE TO MAGNETIZED DIPOLES" 10. I. Problem Find the field components B, and B, in the z and Y directions due to the magnetization M in polar coordinates (Fig. 10.1).

z

FIG. 10.1.

10.2. Solution If 2 and i denote the unit vectors in z and r directions, we get the axial field component : B, = B e , $ (10.1)

and the radial field component:

B,

=

B.r^ ( 10.2)

*Problem 10 is by H. Brechna. 65

66

H. BRECHNA

Expressing Eqs. (10.1) and (10.2) in terms of the angles 0 and @, we may write :

B, = B, =

3M cos @

COS(@

+ 0)- M cos 0

4nJrj

- 3M sin CD

cos(@

+ 0)- M sin 0

4nlrl

(10.3) (10.4)