homework 05-solutions

# homework 05-solutions - howard(cah3459 homework 05...

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howard (cah3459) – homework 05 – Turner – (56705) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd 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 infnite extent. The acceleration oF gravity is 9 . 8m / s 2 and the permittivity oF Free space is 8 . 854 × 10 - 12 C 2 / N · m 2 . 45 . 5 cm θ ˆ ı ˆ 0 . 11 μ C 1g Areal charge density 0 17 μ C / m 2 ±ind the angle θ the thread makes with the vertically charge sheet. Correct answer: 6 . 15029 . Explanation: Let : g =9 . / s 2 , ± 0 =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 . 11 μ C = 1 . 1 × 10 - 7 C , and L = 45 . 5 cm = 0 . 455 m . The length L oF the string is super²uous. Let the tension in the string be denoted by T . The electric feld due to the infnite sheet is constant in the x -direction and is ² E = σ 2 ± 0 ˆ ı. In the ˆ ı and ˆ directions, Force equilibrium tells us T sin θ = q · σ 2 ± 0 T cos θ = mg tan θ = T sin θ T cos θ = q σ 2 m g ± 0 θ = arctan ± 2 m g ± 0 ² = arctan ³ (1 . 1 × 10 - 7 C) (1 . 7 × 10 - 7 C / m 2 ) 2 (0 . 001 kg) (9 . / s 2 ) ± 0 ´ = 6 . 15029 . 002 (part 2 oF 2) 10.0 points What value would σ in order For he angle 85 ? Correct answer: 18 . 0324 μ C / m 2 . Explanation: ±rom the previous part, we know σ = 2 tan θ q ± 0 = 2 (0 . 001 kg) ( 9 . / s 2 ) tan(85 ) 1 . 1 × 10 - 7 C · (8 . 854 × 10 - 12 C 2 / N · m 2 ) 10 6 μ C 1C = 18 . 0324 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 ± 0 = 1 4 π k e . The magnitude oF the resultant electric feld E (where “outside” stands For above and be- low the two plates) is 1. zero between the plates, σ 2 ± 0 outside.

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homework 05-solutions - howard(cah3459 homework 05...

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