894_Physics ProblemsTechnical Physics

894_Physics ProblemsTechnical Physics - 234 P31.61 Faradays...

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234 Faraday’s Law P31.61 The flux through the coil is Φ B BA BA t =⋅ = = BA cos cos θω . The induced emf is ε ω ωω =− = N d dt NBA dt dt NBA t B Φ cos sin bg . (a) εω max .. . . . . == × = NBA 60 0 1 00 0 100 0 200 30 0 36 0 T m r a d s V 2 a f ej (b) d dt N B Φ = , thus d dt N B Φ max max . = = 36 0 0 600 0 600 V 60.0 V W b s (c) At t = 00500 . s , t = 150 . rad and εε = max sin . . sin . . 360 359 rad V rad V af a f . (d) The torque on the coil at any time is τµ =×= ×= = F H G I K J F H G I K J B NI NAB I t R t sin sin max . When = max , sin . t = 1 00 and τ = max . . 2 2 36 0 30 0 10 0 432 R V rad s Nm . P31.62 (a) We use N t B ∆Φ , with N = 1 . Taking a 500 10 3 m to be the radius of the washer, and h = 0500 m , ∆Φ B BA BA AB B a I ha I a aI ha a ahI =−= = + F H G I K J = + F H G I K J = + 21 2 1 2 00 2 22 2 11 2 π µ µµ . The time for the washer to drop a distance h (from rest) is: t h g = 2 . Therefore, = + = + = + 0 2 2 2 ahI hat ahI g h aI gh and = ×⋅ × + = −− 4 10 5 00 10 10 0 2 0 500 0 005 00 980 2 97 4 73 TmA m A m m ms m nV 2 e j (b) Since the magnetic flux going through the washer (into the plane of the paper) is decreasing in time, a current will form in the washer so as to oppose that decrease. Therefore, the
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