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Unformatted text preview: 21. (a) The ﬁeld of a dipole along its axis is given by Eq. 3029:
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 endforend
(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 dipoledipole
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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 Fall '08
 SPRUNGER
 Physics, Energy

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