P32_051 - 1 2 m dx dt 2 + 1 2 kx 2 = const . , which yields...

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51. The interacting potential energy between the magnetic dipole of the compass and the Earth’s magnetic Feld is U = · ~ B e = µB e cos θ ,where θ is the angle between and ~ B e . ±or small angle θ U ( θ )= µB e cos θ ≈− µB e µ 1 θ 2 2 = 1 2 κθ 2 µB e where κ = µB e . Conservation of energy for the compass then gives 1 2 I µ dt 2 + 1 2 κθ 2 =con s t
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Unformatted text preview: 1 2 m dx dt 2 + 1 2 kx 2 = const . , which yields = p k/m . So by analogy, in our case = r I = r B e I = s B e ml 2 / 12 , which leads to = ml 2 2 12 B e = (0 . 050 kg)(4 . 10 2 m) 2 (45 rad / s) 2 12(16 10 6 T) = 8 . 4 10 2 J / T ....
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