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Unformatted text preview: terry (ect328) homework 29 Turner (59130) 1 This print-out should have 10 questions. Multiple-choice 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 1580 turns uni- formly distributed over a length of 0 . 078 m in order to produce a magnetic field of magnitude 0 . 000296 T at the center of the solenoid? The permeability of free space is 4 10 7 T m / A . Correct answer: 11 . 6284 mA. Explanation: Let : N = 1580 , L = 0 . 078 m , B = 0 . 000296 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 . 000296 T) (0 . 078 m) (4 10 7 T m / A) (1580) 1000 mA 1 A = 11 . 6284 mA . 002 10.0 points A single piece of wire is bent into the shape of Texas, with a total area of 7 . 45 cm 2 . This Texas shaped loop is perpendicular to a mag- netic field which increases uniformly in mag- nitude from 0 . 745 T to 2 . 19 T in a time of 2 s. The wire has a total resistance of 4 . What is the current? Correct answer: 0 . 134566 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 . 000745 m 2 )(0 . 7225 T / s) = 0 . 000538262 V . From Faradays Law: E =- d dt =- . 000538262 V From Ohms Law: I = E R = . 000538262 V 4 = 0 . 134566 mA 003 10.0 points A toroid having a rectangular cross section ( a = 1 . 37 cm by b = 4 . 51 cm) and inner radius 2 . 54 cm consists of N = 330 turns of wire that carries a current I = I sin t , with I = 42 . 1 A and a frequency f = 85 . 6 Hz. A loop that consists of N = 21 turns of wire links the toroid, as in the figure....
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- Fall '09