888_Physics ProblemsTechnical Physics

888_Physics ProblemsTechnical Physics - 228 P31.43 Faradays...

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228 Faraday’s Law P31.43 (a) At terminal speed, Mg F IwB R wB Bwv R wB Bwv R B TT == = F H G I K J = F H G I K J = ε 22 or v MgR B T = ω . (b) The emf is directly proportional to v T , but the current is inversely proportional to R. A large R means a small current at a given speed, so the loop must travel faster to get Fm g B = . FIG. P31.43 (c) At a given speed, the current is directly proportional to the magnetic field. But the force is proportional to the product of the current and the field. For a small B , the speed must increase to compensate for both the small B and also the current, so vB T 2 . Section 31.7 Maxwell’s Equations P31.44 Fa E v B == + × mqq so aE v B = e m where ijk j ×= = ±± ± . . . ± 10 0 0 0 00 0 4 0 0 400 ai j j i j j = −× × +− = × + =− × × 160 10 911 10 2 50 5 00 4 00 1 76 10 2 50 1 00 4 39 10 1 76 10 19 31 11 11 11 . . . ± . ± . ± .. ± . ± . ± . ± ej ms 2 P31.45 E v B + × v B =+ × e m where ij k jk = + ±±± ... . ± . ± 200 0 0 0 200 0 300 0 400 200 0 400
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