# HW 05 - saldana (avs387) – homework 05 – Turner –...

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Unformatted text preview: saldana (avs387) – homework 05 – Turner – (56705) 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 . 7 3 . 6 c m θ ˆ ı ˆ . 15 μ C 1 g A r e a l c h a r g e d e n s i t y . 2 8 μ C / m 2 Find the angle θ the thread makes with the vertically charge sheet. Correct answer: 13 . 6052 ◦ . 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 . 28 μ C / m 2 = 2 . 8 × 10 − 7 C / m 2 , q = 0 . 15 μ C = 1 . 5 × 10 − 7 C , and L = 73 . 6 cm = 0 . 736 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 (1 . 5 × 10 − 7 C) (2 . 8 × 10 − 7 C / m 2 ) 2 (0 . 001 kg) (9 . 8 m / s 2 ) ǫ bracketrightbigg = 13 . 6052 ◦ . 002 (part 2 of 2) 10.0 points What value would σ in order for he angle 84 ◦ ? Correct answer: 11 . 0075 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(84 ◦ ) 1 . 5 × 10 − 7 C · (8 . 854 × 10 − 12 C 2 / N · m 2 ) 10 6 μ C 1 C = 11 . 0075 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 10/26/2010 for the course PHYS 56705 taught by Professor Turner during the Spring '10 term at University of Texas at Austin.

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HW 05 - saldana (avs387) – homework 05 – Turner –...

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