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Unformatted text preview: brown (twb493) Ch16-h1 chiu (56565) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 6) 5.0 points A plastic rod 1 . 8 m long is rubbed all over with wool, and acquires a charge of 4 10- 8 C (see the figure below). We choose the center of the rod to be the origin of our coordinate system, with the x axis extending to the right, the y axis extending up, and the z axis out of the page. In order to calculate the electric field at location A , which is at vectorr A = ( . 5 , , ) m , we divide the rod into 8 pieces, and approxi- mate each piece as a point charge located at the center of the piece. b A 1 2 3 4 5 6 7 8 What is the length of one of these pieces? Use the value of k = 8 . 98755 10 9 N m 2 / C 2 . Correct answer: 0 . 225 m. Explanation: We simply divide the length of the rod by 8: y = (1 . 8 m) / 8 = 0 . 225 m . 002 (part 2 of 6) 5.0 points What is the y coordinate of the center of piece number 4? Correct answer: 0 . 1125 m. Explanation: Since the center of the rod is at (0,0,0) and it lies along the y axis, we know that only the y coordinate changes as we move along the rod. To find the y coordinate of the center of this particular piece, we just add the lower and upper y bounds of the piece and divide by 2: r center , 4 y = r lower , 4 y + r upper , 4 y 2 = 0 m + (0 . 225 m) 2 = . 1125 m . 003 (part 3 of 6) 5.0 points How much charge is on piece number 4? (Re- member that the charge is negative.) Correct answer: 5 10- 9 C. Explanation: As in the first part of this problem, we know the total charge, so to find the charge on any particular piece, we simply divide by 8: Q = 4 10- 8 C / 8 = 5 10- 9 C . 004 (part 4 of 6) 5.0 points Approximating piece 4 as a point charge, what is the electric field at location A due only to piece 4? This is a vector with x and y components, vector E ( A ) = ( E ( A ) x , E ( A ) y , ) N / C , so begin by finding the x component, E ( A ) x . Correct answer: 166 . 917 N / C. Explanation: The electric field of a point charge is given by the familiar expression vector E ( A ) = 1 4 q | vectorr | 2 r. So we need the total distance between the piece we are considering and the location A , brown (twb493) Ch16-h1 chiu (56565) 2 and also the unit vector pointing from the piece to A . The distance is easy to find: | vectorr | = radicalBig (0 . 1125 m) 2 + (0 . 5 m) 2 = 0 . 5125 m . The unit vectors components are r = ( . 5 , . 1125 , ) m . 5125 m = ( . 97561 , . 219512 , ) . The x component of the field, then, is E ( A ) x = 1 4 5 10- 9 C (0 . 5125 m) 2 (0 . 97561) = 166 . 917 N / C ....
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This note was uploaded on 12/01/2011 for the course PHY 303L taught by Professor Turner during the Fall '08 term at University of Texas at Austin.
- Fall '08