Page 270 - Engineering Electromagnetics, 8th Edition

252 ENGINEERING ELECTROMAGNETICS

values of µ r would range from 10 to 100, 000. Diamagnetic, paramagnetic, and
antiferromagnetic materials are commonly said to be nonmagnetic.

D8.6. Find the magnetization in a magnetic material where: (a) µ = 1.8 ×
3
28
10 −5 H/m and H = 120 A/m; (b) µ r = 22, there are 8.3 × 10 atoms/m , and
2
each atom has a dipole moment of 4.5 × 10 −27 A · m ;(c) B = 300 µT and
χ m = 15.
Ans. 1599 A/m; 374 A/m; 224 A/m

D8.7. The magnetization in a magnetic material for which χ m = 8isgivenin
2
a certain region as 150z a x A/m. At z = 4 cm, find the magnitude of: (a) J T ;
(b)J;(c) J B .
2
2
Ans. 13.5 A/m ; 1.5 A/m ;12A/m 2

8.7 MAGNETIC BOUNDARY CONDITIONS
We should have no difficulty in arriving at the proper boundary conditions to apply to
B, H, and M at the interface between two different magnetic materials, for we have
solved similar problems for both conducting materials and dielectrics. We need no
new techniques.
Figure 8.10 shows a boundary between two isotropic homogeneous linear materi-
als with permeabilities µ 1 and µ 2 . The boundary condition on the normal components

Figure 8.10 A gaussian surface and a closed path are
constructed at the boundary between media 1 and 2, having
permeabilities of µ 1 and µ 2 ,respectively. From this we determine the
boundary conditions B N1 = B N2 and H t1 − H t2 = K , the component
of the surface current density directed into the page.