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Hw4_pdf - mcconnell(kam2342 – homework04 – Turner...

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mcconnell (kam2342) – homework04 – Turner – (60230) 1 This print-out should have 11 questions. Multiple-choice 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 0 on the x axis? Assume that x 0 > x 2 > x 1 and k e = 1 4 πǫ 0 . 1. integraldisplay x 2 x 1 k e Q ( x 2 x 1 )( x 0 x ) 2 dx correct 2. integraldisplay x 2 x 1 k e Q ( x 2 x 0 )( x 0 x ) 2 dx 3. integraldisplay x 2 x 1 k e Q ( x 2 x 1 ) x 2 dx 4. None of these 5. integraldisplay x 2 x 1 k e Q ( x 2 x 0 ) 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 0 is a distance ( x 0 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 0 x ) 2 dx . 002 (part 2 of 2) 10.0 points If x 1 = 0 m, x 2 = 3 . 36 m and the charge Q = 2 . 44 μ C, what is the magnitude E of the electric field at x 0 = 10 . 7 m? Correct answer: 279 . 223 N / C. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , x 1 = 0 m , x 2 = 3 . 36 m , x 0 = 10 . 7 m , and Q = 2 . 44 μ C . E = integraldisplay x 2 x 1 k e Q ( x 2 x 1 )( x 0 x ) 2 dx = k e Q ( x 2 x 1 )( x 0 x ) vextendsingle vextendsingle vextendsingle vextendsingle x 2 x 1 = ( 8 . 98755 × 10 9 N · m 2 / C 2 ) (3 . 36 m 0 m) × (2 . 44 × 10 6 C) × bracketleftbigg 1 10 . 7 m 3 . 36 m 1 10 . 7 m 0 m bracketrightbigg = 279 . 223 N / C . 003 (part 1 of 4) 10.0 points Consider a disk of radius 3 cm, having a uni- formly distributed charge of +5 μ C. The value of the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . Compute the magnitude of the electric field at a point on the axis and 2 . 6 mm from the center. Correct answer: 9 . 12393 × 10 7 N / C.
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