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Ch16-h1-solutions - liu(ql744 Ch16-h1 chiu(56565 This...

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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 . 5 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 r A = 0 . 9 , 0 , 0 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 . 1875 m. Explanation: We simply divide the length of the rod by 8: Δ y = (1 . 5 m) / 8 = 0 . 1875 m . 002 (part 2 of 6) 5.0 points What is the y coordinate of the center of piece number 6? Correct answer: - 0 . 28125 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 = - 0 . 375 m + ( - 0 . 1875 m) 2 = - 0 . 28125 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: - 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 = - 4 × 10 - 8 C / 8 = - 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 , 0 N / C , so begin by finding the x component, E ( A ) x . Correct answer: - 48 . 2422 N / C. Explanation: The electric field of a point charge is given by the familiar expression E ( A ) = 1 4 πε 0 q | r | 2 ˆ r.
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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 | = ( - 0 . 28125 m) 2 + (0 . 9 m) 2 = 0 . 942922 m . The unit vector’s components are ˆ r = 0 . 9 , 0 . 28125 , 0 m 0 . 942922 m = 0 . 95448 , 0 . 298275 , 0 . The x component of the field, then, is E ( A ) x = 1 4 πε 0 - 5 × 10 - 9 C (0 . 942922 m) 2 (0 . 95448) = - 48 . 2422 N / C . 005 (part 5 of 6) 5.0 points Find E ( A ) y . Correct answer: - 15 . 0757 N / C. Explanation: This is just like part 4, except with respect to the y components: E ( A ) y = 1 4 πε 0 - 5 × 10 - 9 C (0 . 942922 m) 2 (0 . 298275) = - 15 . 0757 N / C . 006 (part 6 of 6) 5.0 points To get the net electric field at location A , we would need to calculate Δ E due to each of the 8 pieces, and add up these contributions. If we did that, which arrow (I-VIII) on the following diagram would best represent the direction of the net electric field at location A ?
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