solutio3474n7_pdf - kinsey (cbk323) – homework 05 –...

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Unformatted text preview: kinsey (cbk323) – homework 05 – Turner – (56725) 1 This print-out should have 12 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 charged mass on the end of a light string is attached to a point on a uniformly charged vertical sheet of infinite extent. The acceleration of gravity is 9 . 8 m / s 2 and the permittivity of free space is 8 . 854 × 10 − 12 C 2 / N · m 2 . 8 6 c m θ ˆ ı ˆ . 3 μ C 1 g A r e a l c h a r g e d e n s i t y . 1 7 μ C / m 2 Find the angle θ the thread makes with the vertically charge sheet. Correct answer: 16 . 3772 ◦ . Explanation: Let : g = 9 . 8 m / s 2 , ǫ = 8 . 854 × 10 − 12 C 2 / N · m 2 , m = 1 g = 0 . 001 kg , σ = 0 . 17 μ C / m 2 = 1 . 7 × 10 − 7 C / m 2 , q = 0 . 3 μ C = 3 × 10 − 7 C , and L = 86 cm = 0 . 86 m . The length L of the string is superfluous. Let the tension in the string be denoted by T . The electric field due to the infinite sheet is constant in the x-direction and is vector E = σ 2 ǫ ˆ ı . In the ˆ ı and ˆ directions, force equilibrium tells us T sin θ = q · σ 2 ǫ T cos θ = m g tan θ = T sin θ T cos θ = q σ 2 m g ǫ θ = arctan parenleftbigg q σ 2 m g ǫ parenrightbigg = arctan bracketleftbigg (3 × 10 − 7 C) (1 . 7 × 10 − 7 C / m 2 ) 2 (0 . 001 kg) (9 . 8 m / s 2 ) ǫ bracketrightbigg = 16 . 3772 ◦ . 002 (part 2 of 2) 10.0 points What value would σ in order for he angle 82 ◦ ? Correct answer: 4 . 11598 μ C / m 2 . Explanation: From the previous part, we know σ = 2 m g tan θ q ǫ = 2 (0 . 001 kg) ( 9 . 8 m / s 2 ) tan(82 ◦ ) 3 × 10 − 7 C · (8 . 854 × 10 − 12 C 2 / N · m 2 ) 10 6 μ C 1 C = 4 . 11598 μ C / m 2 . 003 10.0 points Two large, parallel, insulating plates are charged uniformly with the same positive areal charge density + σ , which is the charge per unit area. The permittivity of free space ǫ = 1 4 π k e ....
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This note was uploaded on 11/02/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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solutio3474n7_pdf - kinsey (cbk323) – homework 05 –...

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