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829_Physics ProblemsTechnical Physics

829_Physics ProblemsTechnical Physics - Chapter 29 P29.25...

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Chapter 29 169 P29.25 Choose U = 0 when the dipole moment is at θ = ° 90 0 . to the field. The field exerts torque of magnitude µ θ B sin on the dipole, tending to turn the dipole moment in the direction of decreasing θ . According to Equations 8.16 and 10.22, the potential energy of the dipole-field system is given by U B d B B = = = − + ° ° z 0 0 90 0 90 0 µ θ θ µ θ µ θ θ θ sin cos cos . . a f or U = − µ B . P29.26 (a) The field exerts torque on the needle tending to align it with the field, so the minimum energy orientation of the needle is: pointing north at 48.0 below the horizontal ° where its energy is U B min cos . . . = − °= − × × = − × µ 0 9 70 10 55 0 10 5 34 10 3 6 7 A m T J 2 e je j . It has maximum energy when pointing in the opposite direction, south at 48.0 above the horizontal ° where its energy is U B max cos . . . = − °= + × × = + × µ 180 9 70 10 55 0 10 5 34 10 3 6 7 A m T J 2 e je j . (b) U W U min max + = : W U U = = + × − − × = max min . . . 5 34 10 5 34 10 1 07 7 7 J J J e j µ P29.27 (a) τ = × µ B , so τ µ θ θ = × = = µ B B NIAB sin sin τ π µ max sin . . . . = °= × = NIAB 90 0 1 5 00 0 050 0 3 00 10 118 2 3 A m T N m a f b g e j (b) U = − µ B , so ≤ + µ µ B
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