Ch16-h1-solutions

# Ch16-h1-solutions - pan (zp695) – Ch16-h1 – chiu –...

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Unformatted text preview: pan (zp695) – 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 . 9 m long is rubbed all over with wool, and acquires a charge of- 2 × 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 r 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. 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 . 2375 m. Explanation: We simply divide the length of the rod by 8: Δ y = (1 . 9 m) / 8 = 0 . 2375 m . 002 (part 2 of 6) 5.0 points What is the y coordinate of the center of piece number 6? Correct answer:- . 35625 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 , 6 y = r lower , 6 y + r upper , 6 y 2 =- . 475 m + (- . 2375 m) 2 =- . 35625 m . 003 (part 3 of 6) 5.0 points How much charge is on piece number 6? (Re- member that the charge is negative.) Correct answer:- 2 . 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: Δ Q =- 2 × 10- 8 C / 8 =- 2 . 5 × 10- 9 C . 004 (part 4 of 6) 5.0 points Approximating piece 6 as a point charge, what is the electric field at location A due only to piece 6? This is a vector with x and y components, E ( A ) = E ( A ) x , E ( A ) y , N / C , so begin by finding the x component, E ( A ) x . Correct answer:- 48 . 5498 N / C. Explanation: The electric field of a point charge is given by the familiar expression E ( A ) = 1 4 πε q | r | 2 ˆ r. pan (zp695) – Ch16-h1 – chiu – (56565) 2 So we need the total distance between the piece we are considering and the location A , and also the unit vector pointing from the piece to A . The distance is easy to find: | r | = (- . 35625 m) 2 + (0 . 5 m) 2 = 0 . 613933 m . The unit vector’s components are ˆ r = . 5 , . 35625 , m . 613933 m = . 814421 , . 580275 , . The x component of the field, then, is E ( A ) x = 1 4 πε- 2 . 5 × 10- 9 C (0 . 613933 m) 2 (0 . 814421) =- 48 . 5498 N / C ....
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## This note was uploaded on 02/21/2012 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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Ch16-h1-solutions - pan (zp695) – Ch16-h1 – chiu –...

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