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# HW 4 - Kapoor(mk9499 homework04 Turner(60230 This print-out...

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Kapoor (mk9499) – 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. None of these 2. integraldisplay x 2 x 1 k e Q ( x 2 x 1 ) x 2 dx 3. integraldisplay x 2 x 1 k e Q ( x 2 x 0 ) x 2 dx 4. integraldisplay x 2 x 1 k e Q ( x 2 x 0 )( x 0 x ) 2 dx 5. integraldisplay x 2 x 1 k e Q ( x 2 x 1 )( x 0 x ) 2 dx correct 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 = 5 . 59 m and the charge Q = 3 . 49 μ C, what is the magnitude E of the electric field at x 0 = 8 . 2 m? Correct answer: 1465 . 59 N / C. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , x 1 = 0 m , x 2 = 5 . 59 m , x 0 = 8 . 2 m , and Q = 3 . 49 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 ) (5 . 59 m 0 m) × (3 . 49 × 10 6 C) × bracketleftbigg 1 8 . 2 m 5 . 59 m 1 8 . 2 m 0 m bracketrightbigg = 1465 . 59 N / C . 003 (part 1 of 4) 10.0 points Consider a disk of radius 3 . 1 cm, having a uniformly distributed charge of +5 . 7 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 3 . 6 mm from the center. Correct answer: 9 . 43175 × 10 7 N / C.

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