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879_Physics ProblemsTechnical Physics

879_Physics ProblemsTechnical Physics - 219 Chapter...

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Chapter 31 219 *P31.14 (a) Each coil has a pulse of voltage tending to produce counterclockwise current as the projectile approaches, and then a pulse of clockwise voltage as the projectile recedes. (b) v d t = = × = 1 50 10 625 3 . m 2.40 s m s V 1 V 2 t 0 V FIG. P31.14 P31.15 ε θ θ = = d dt NB N B t A A 2 2 cos cos e j A = = × × × ° = ε θ t N B cos . . cos . . 80 0 10 0 400 50 600 10 200 10 30 0 1 36 3 6 6 V s T T m e j a f a f e j a f Length = = = 4 4 1 36 50 272 A N . m m a fa f *P31.16 (a) Suppose, first, that the central wire is long and straight. The enclosed current of unknown amplitude creates a circular magnetic field around it, with the magnitude of the field given by Ampere’s Law. B s = z d I µ 0 : B I t R = µ ω π 0 2 max sin at the location of the Rogowski coil, which we assume is centered on the wire. This field passes perpendicularly through each turn of the toroid, producing flux B A = µ ω π 0 2 I A t R max sin . The toroid has 2 π Rn turns. As the magnetic field varies, the emf induced in it is ε π µ π ω µ ω ω = − = − = − N d dt Rn I A R d dt t I nA t B A 2 2 0 0 max max sin cos . This is an alternating voltage with amplitude
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