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hw15 - Physics 21 Fall 2004 Solution to HW-15 29 P 21...

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Physics 21 Fall, 2004 Solution to HW-15 29 P 21 Determine the magnetic ﬂux through a square loop of side a if one side is parallel to, and a distance a from, a straight wire that carries a current I . The field of the wire is B ( r ) = µ 0 I/ 2 πr , directed perpen- dicular to the loop. The ﬂux is Φ = 2 a a B ( r ) a dr = µ 0 I 2 π a 2 a a dr r The definite integral is 2 a a dr r = ln r | 2 a a = ln 2 a ln a = ln 2 a a = ln 2 Combining terms, we obtain Φ = µ 0 Ia 2 π ln 2 0 . 6931 µ 0 Ia 2 π . One can get a pretty good approximate answer by assuming B ( r ) is constant over the loop and taking the value at the middle, where r = 1 . 5 a . Then Φ = B (1 . 5 a ) a 2 = µ 0 I 2 π (1 . 5 a ) a 2 = 2 3 µ 0 Ia 2 π 0 . 6667 µ 0 Ia 2 π . 29 P 40 Neon signs require 12 kV for their operation. To operate from a 220 V line, what must be the ratio of sec- ondary to primary turns of the transformer? What would be the voltage output if the transformer were connected back- ward? Given that V P = 12 kV and V S = 220 V, we can use V S V P = 12 , 000 220 = N S N P = 54 . 5
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