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Unformatted text preview: terry (ect328) – homework 04 – Turner – (59130) 1 This printout should have 11 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 (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 πǫ . 1. integraldisplay x 2 x 1 k e Q ( x 2 − x 1 )( x − x ) 2 dx correct 2. None of these 3. integraldisplay x 2 x 1 k e Q ( x 2 − x ) x 2 dx 4. integraldisplay x 2 x 1 k e Q ( x 2 − x )( x − x ) 2 dx 5. integraldisplay x 2 x 1 k e Q ( x 2 − x 1 ) 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 = λ 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 . 002 (part 2 of 2) 10.0 points If x 1 = 0 m, x 2 = 3 . 37 m and the charge Q = 2 . 23 μ C, what is the magnitude E of the electric field at x = 10 . 1 m? Correct answer: 294 . 856 N / C. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , x 1 = 0 m , x 2 = 3 . 37 m , x = 10 . 1 m , and Q = 2 . 23 μ C . 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 ) (3 . 37 m − 0 m) × (2 . 23 × 10 − 6 C) × bracketleftbigg 1 10 . 1 m − 3 . 37 m − 1 10 . 1 m − 0 m bracketrightbigg = 294 . 856 N / C . 003 (part 1 of 4) 10.0 points Consider a disk of radius 2 . 7 cm with a uni formly distributed charge of +4 . 8 μ C. Compute the magnitude of the electric field at a point on the axis and 2 . 5 mm from the center. The value of the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 ....
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 Fall '09
 Turner
 Electrostatics, Electric charge, Terry, KE, Etot

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