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Unformatted text preview: Kapoor (mk9499) HW 03 Turner (60230) 1 This printout should have 14 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points The diagram shows an isolated, positive charge Q , where point B is twice as far away from Q as point A . + Q A B 10 cm 20 cm The ratio of the electric field strength at point A to the electric field strength at point B is 1. E A E B = 8 1 . 2. E A E B = 4 1 . correct 3. E A E B = 1 1 . 4. E A E B = 2 1 . 5. E A E B = 1 2 . Explanation: Let : r B = 2 r A . The electric field strength E 1 r 2 , so E A E B = 1 r 2 A 1 r 2 B = r 2 B r 2 A = (2 r ) 2 r 2 = 4 . 002 (part 1 of 2) 10.0 points A charge Q is distributed uniformly along the x axis from x 1 to x 2 . The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 Which of the following integrals is correct for the magnitude of the electric field at x on the x axis? Assume that x > x 2 > x 1 and k e = 1 4 . 1. integraldisplay x 2 x 1 k e Q ( x 2 x 1 ) x 2 dx 2. integraldisplay x 2 x 1 k e Q ( x 2 x 1 )( x x ) 2 dx correct 3. integraldisplay x 2 x 1 k e Q ( x 2 x ) x 2 dx 4. None of these 5. integraldisplay x 2 x 1 k e Q ( x 2 x )( x x ) 2 dx Explanation: For a continuous charge distribution, dE = k e dq r 2 . Recall that for a uniform linear charge dis tribution, dq = dx = Q L dx = Q x 2 x 1 dx . Furthermore, the point x is a distance ( x x ) from a charge element dq . Hence integrating from x = x 1 to x = x 2 yields E = integraldisplay x 2 x 1 k e Q ( x 2 x 1 )( x x ) 2 dx . 003 (part 2 of 2) 10.0 points If x 1 = 0 m, x 2 = 5 . 73 m and the charge Q = 4 . 24 C, what is the magnitude E of the electric field at x = 8 . 5 m? Correct answer: 1618 . 48 N / C. Explanation: Let : k e = 8 . 98755 10 9 N m 2 / C 2 , x 1 = 0 m , x 2 = 5 . 73 m , x = 8 . 5 m , and Q = 4 . 24 C . Kapoor (mk9499) HW 03 Turner (60230) 2 E = integraldisplay x 2 x 1 k e Q ( x 2 x 1 )( x x ) 2 dx = k e Q ( x 2 x 1 )( x x ) vextendsingle vextendsingle vextendsingle vextendsingle x 2 x 1 = ( 8 . 98755 10 9 N m 2 / C 2 ) (5 . 73 m 0 m) (4 . 24 10 6 C) bracketleftbigg 1 8 . 5 m 5 . 73 m 1 8 . 5 m 0 m bracketrightbigg = 1618 . 48 N / C ....
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 Fall '08
 Turner
 Physics, Charge

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