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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 π × 10 − 7 T · m / A . Correct answer: 10 . 2021 mA. Explanation: Let : N = 2750 , L = 0 . 312 m , B = 0 . 000113 T , and μ = 4 π × 10 − 7 T · m / A . The magnetic field inside a long solenoid is B = μ n I = μ parenleftbigg N L parenrightbigg I . Thus the required current is I = B L μ N = (0 . 000113 T) (0 . 312 m) (4 π × 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 Ω. What is the current? Correct answer: 0 . 0756993 mA. Explanation: Basic Concepts: Faraday’s Law of Induc tion: E = d Φ 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 Φ = B A . d Φ dt = d dt ( B A ) = A d B dt = A Δ B Δ t = A B 2 B 1 Δ t = (0 . 000542 m 2 )(0 . 419 T / s) = 0 . 000227098 V . From Faraday’s Law: E = d Φ dt = . 000227098 V From Ohm’s Law: I = E R = . 000227098 V 3 Ω = 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 ω t , with I = 42 A and a frequency f = 69 . 9 Hz. A loop that consists of N ℓ = 31 turns of wire links the toroid, as in the figure....
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This note was uploaded on 01/21/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas.
 Spring '08
 Turner
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