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Unformatted text preview: 21. (a) The ﬁeld of a dipole along its axis is given by Eq. 30-29:
B= µ0 µ
2π z 3 where µ is the dipole moment and z is the distance from the dipole. Thus,
B= (4π × 10−7 T · m/A)(1.5 × 10−23 J/T)
= 3.0 × 10−6 T .
2π (10 × 10−9 m) (b) The energy of a magnetic dipole µ in a magnetic ﬁeld B is given by U = −µ · B = −µB cos φ, where
φ is the angle between the dipole moment and the ﬁeld. The energy required to turn it end-for-end
(from φ = 0◦ to φ = 180◦ ) is
∆U = 2µB = 2(1.5 × 10−23 J/T)(3.0 × 10−6 T) = 9.0 × 10−29 J = 5.6 × 10−10 eV .
The mean kinetic energy of translation at room temperature is about 0.04 eV. Thus, if dipole-dipole
interactions were responsible for aligning dipoles, collisions would easily randomize the directions
of the moments and they would not remain aligned. ...
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