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Unformatted text preview: gonzales (pag757) Homework 2 Hoffmann (56745) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A rod 6 . 1 cm long is uniformly charged and has a total charge of 15 C. Determine the magnitude of the elec tric field along the axis of the rod at a point 36 . 1231 cm from the center of the rod. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 . Correct answer: 1 . 04057 10 6 N / C. Explanation: Let : = 6 . 1 cm , Q = 15 C , r = 36 . 1231 cm , and k e = 8 . 98755 10 9 N m 2 / C 2 . For a rod of length and linear charge density (charge per unit length) , the field at a dis tance d from the end of the rod along the axis is E = k e integraldisplay d + d x 2 dx = k e x vextendsingle vextendsingle vextendsingle vextendsingle d + d = k e d ( + d ) , where dq = dx . The linear charge density (if the total charge is Q ) is = Q so that E = k e Q d ( + d ) = k e Q d ( + d ) . In this problem, we have the following situa tion (the distance r from the center is given): d l r r The distance d is d = r 2 = 36 . 1231 cm 6 . 1 cm 2 = 0 . 330731 m , and the magnitude of the electric field is E = k e Q d ( + d ) = ( 8 . 98755 10 9 N m 2 / C 2 )  1 . 5 10 5 C  (0 . 330731 m)(0 . 061 m + 0 . 330731 m) = 1 . 04057 10 6 N / C . Now, the direction must be toward the rod, since the charge distribution is negative (a positive test charge would be attracted). So the sign should be positive, according to the convention stated in the problem. keywords: 002 10.0 points A 9 . 6 g piece of Styrofoam carries a net charge of . 5 C and floats above the center of a very large horizontal sheet of plastic that has a uniform charge density on its surface. The acceleration of gravity is 9 . 8 m / s 2 and the permittivity of free space is 8 . 85419 10 12 C 2 / N / m 2 . What is the charge per unit area on the plastic sheet? Correct answer: 3 . 33201 C / m 2 . Explanation: Let : m = 9 . 6 g , q = . 5 C , g = 9 . 8 m / s 2 , and = 8 . 85419 10 12 C 2 / N / m 2 . gonzales (pag757) Homework 2 Hoffmann (56745) 2 The field due to a nonconducting infinite sheet of charge is the same as that very close to any plane uniform charge distribution. The field is E = 2...
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This note was uploaded on 01/27/2012 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
 Charge, Work

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