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897_Physics ProblemsTechnical Physics

# 897_Physics ProblemsTechnical Physics - Chapter 31 P31.71...

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Chapter 31 237 P31.71 The magnetic field produced by the current in the straight wire is perpendicular to the plane of the coil at all points within the coil. The magnitude of the field is B I r = µ π 0 2 . Thus, the flux linkage is N NIL dr r NI L h w h t B h h w Φ = = + F H G I K J + + z µ π µ π ω φ 0 0 2 2 max ln sin b g . Finally, the induced emf is FIG. P31.71 ε µ ω π ω φ ε π π π ω φ ε π φ = − + F H G I K J + = − × + F H G I K J + = + 0 7 1 2 1 4 10 100 50 0 0 200 200 2 1 5 00 87 1 200 NI L w h t t t max ln cos . . ln . cos . cos b g e j a fa fa f e j b g a f b g m s cm 5.00 cm mV The term sin ω φ t + b g in the expression for the current in the straight wire does not change appreciably when ω t changes by 0.10 rad or less. Thus, the current does not change appreciably during a time interval t < = × 0 10 200 1 6 10 1 4 . . π s s e j . We define a critical length, c t ∆ = × × = × 3 00 10 1 6 10 4 8 10 8 4 4 . . . m s s m e je j equal to the distance to which field changes could be propagated during an interval of 1 6 10 4 . × s . This length is so much larger than any dimension of the coil or its distance from the wire that, although we consider the
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