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917_Physics ProblemsTechnical Physics

# 917_Physics ProblemsTechnical Physics - Chapter 32 P32.67...

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Chapter 32 257 P32.67 From Ampere’s law, the magnetic field at distance r R is found as: B r J r I R r 2 0 2 0 2 2 π µ π µ π π b g e j e j = = F H G I K J , or B Ir R = µ π 0 2 2 . The magnetic energy per unit length within the wire is then U B rdr I R r dr I R R I R R A = = = F H G I K J = z z 2 0 0 0 2 4 3 0 0 2 4 4 0 2 2 2 4 4 4 16 µ π µ π µ π µ π b g . This is independent of the radius of the wire. P32.68 The primary circuit (containing the battery and solenoid) is an RL circuit with R = 14 0 . , and L N A = = × × = µ π 0 2 7 2 4 4 10 12 500 1 00 10 0 070 0 0 280 A e j b g e j . . . H . (a) The time for the current to reach 63.2% of the maximum value is the time constant of the circuit: τ = = = = L R 0 280 0 020 0 20 0 . . . H 14.0 s ms . (b) The solenoid’s average back emf is ε L f L I t L I t = F H G I K J = F H G I K J 0 FIG. P32.68 where I I V R f = = F H G I K J = F H G I K J = 0 632 0 632 0 632 60 0 2 71 . . . . . max V 14.0 A . Thus, ε L = F H G I K J = 0 280 2 71 37 9 . . . H A 0.020 0 s V a f . (c) The average rate of change of flux through each turn of the overwrapped concentric coil is
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