Magnetic Dipole and Permeable Medium

A point magnetic dipole m in vacuum (medium 1) is pointing toward the plane surface of a medium with permeability μ (medium 2). The distance between the dipole and surface is d (see Figure 1.1).

Figure 1.1

a) Solve for the magnetic field B within the medium.

b) What is the force acting on the dipole?

SOLUTION

a) Use the method of images. We place another dipole m' = α m at the point O', at the same distance d on the other side of the plane separating the vacuum from the permeable medium (see Figure 1.2). Compute the field in medium 1 as a superposition of the dipole fields from m and m'. To find the field in medium 2, we put yet another dipole m'' = β m at point O. We can write this in the form

(1)

(2)

where n, n' are unit vectors in the directions r, r' respectively, and indices 1 and 2 correspond to media 1 and 2. As usual, we write the boundary

Figure 1.2

conditions at some point P on the plane where |r| = |r'|

(3)

(4)

Substituting (1) and (2) into (3) and (4), we obtain

(5)

(6)

From (5) and (6), we have

(7)

which yield

So the field in medium 2 is

b) The force acting on a dipole m is determined only by the field B^(1)' of the image dipole m' in medium 2

(8)

The dipole is attracted to the medium. The result for the equivalent problem of an electric dipole near a half space filled with an ideal conductor can be obtained from (8) by letting μ → ∞

where p is the electric dipole moment.

مواضيع ذات صلة

مصطلحات الفيزياء النووية

إزاحة حمراء REDSHIFT

المركبات النانوية (Nanocomposites)

مولد فان دي جراف الالكتروستاتي

التطويرات التقنية الحديثة في المعجلات الالكتروستاتية

معجلات الالكترونات الالكتروستاتية

معجلات الفان دي جراف الترادفية

الحد من زيادة الطاقة في معجل فان دي جراف

أنبوبة التعجيل قي معجلات الجسيمات من نوع فان دي جراف

ارتكاز معجل فان دي جراف

مبدأ تشغيل معجل الفان دي جراف

القضايا الأخلاقية المتعلقة بتكنولوجيا النانو