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Unformatted text preview: nguyen (jmn727) homework 29 Turner (59070) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points What current is required in the windings of a long solenoid that has 2750 turns uni formly distributed over a length of 0 . 312 m in order to produce a magnetic field of magnitude 0 . 000113 T at the center of the solenoid? The permeability of free space is 4 10 7 T m / A . Correct answer: 10 . 2021 mA. Explanation: Let : N = 2750 , L = 0 . 312 m , B = 0 . 000113 T , and = 4 10 7 T m / A . The magnetic field inside a long solenoid is B = n I = parenleftbigg N L parenrightbigg I . Thus the required current is I = B L N = (0 . 000113 T) (0 . 312 m) (4 10 7 T m / A) (2750) 1000 mA 1 A = 10 . 2021 mA . 002 10.0 points A single piece of wire is bent into the shape of Texas, with a total area of 5 . 42 cm 2 . This Texas shaped loop is perpendicular to a mag netic field which increases uniformly in mag nitude from 0 . 812 T to 1 . 65 T in a time of 2 s. The wire has a total resistance of 3 . What is the current? Correct answer: 0 . 0756993 mA. Explanation: Basic Concepts: Faradays Law of Induc tion: E = d B dt The particular shape of the wire is unimpor tant, only the area enclosed by the wire mat ters. The magnetic flux through the loop is given by = B A . d dt = d dt ( B A ) = A d B dt = A B t = A B 2 B 1 t = (0 . 000542 m 2 )(0 . 419 T / s) = 0 . 000227098 V . From Faradays Law: E = d dt = . 000227098 V From Ohms Law: I = E R = . 000227098 V 3 = 0 . 0756993 mA 003 10.0 points A toroid having a rectangular cross section ( a = 1 . 11 cm by b = 4 . 06 cm) and inner radius 4 . 95 cm consists of N = 440 turns of wire that carries a current I = I sin t , with I = 42 A and a frequency f = 69 . 9 Hz. A loop that consists of N = 31 turns of wire links the toroid, as in the figure....
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 Spring '08
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