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# 303L-HW4 - fierro(jmf2547 – HW 04 – berk –(60290 1...

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Unformatted text preview: fierro (jmf2547) – HW 04 – berk – (60290) 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 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 ) x 2 dx 2. integraldisplay x 2 x 1 k e Q ( x 2 − x )( x − x ) 2 dx 3. integraldisplay x 2 x 1 k e Q ( x 2 − x 1 )( x − x ) 2 dx correct 4. integraldisplay x 2 x 1 k e Q ( x 2 − x 1 ) x 2 dx 5. None of these 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 . 45 m and the charge Q = 2 . 72 μ C, what is the magnitude E of the electric field at x = 8 . 4 m? Correct answer: 587 . 93 N / C. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , x 1 = 0 m , x 2 = 3 . 45 m , x = 8 . 4 m , and Q = 2 . 72 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 . 45 m − 0 m) × (2 . 72 × 10 − 6 C) × bracketleftbigg 1 8 . 4 m − 3 . 45 m − 1 8 . 4 m − 0 m bracketrightbigg = 587 . 93 N / C . 003 (part 1 of 4) 10.0 points Consider a disk of radius 2 cm, having a uni- formly distributed charge of +4 . 5 μ C. The value of the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 ....
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303L-HW4 - fierro(jmf2547 – HW 04 – berk –(60290 1...

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