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# 303L-HW5 - fierro(jmf2547 – HW 05 – berk –(60290 1...

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Unformatted text preview: fierro (jmf2547) – HW 05 – berk – (60290) 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 . 1 c m θ ˆ ı ˆ . 34 μ C 1 g A r e a l c h a r g e d e n s i t y . 1 2 μ C / m 2 Find the angle θ the thread makes with the vertically charge sheet. Correct answer: 13 . 2303 ◦ . 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 . 12 μ C / m 2 = 1 . 2 × 10 − 7 C / m 2 , q = 0 . 34 μ C = 3 . 4 × 10 − 7 C , and L = 73 . 1 cm = 0 . 731 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 . 4 × 10 − 7 C) (1 . 2 × 10 − 7 C / m 2 ) 2 (0 . 001 kg) (9 . 8 m / s 2 ) ǫ bracketrightbigg = 13 . 2303 ◦ . 002 (part 2 of 2) 10.0 points What value would σ in order for he angle 79 ◦ ? Correct answer: 2 . 62582 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(79 ◦ ) 3 . 4 × 10 − 7 C · (8 . 854 × 10 − 12 C 2 / N · m 2 ) 10 6 μ C 1 C = 2 . 62582 μ C / m 2 . 003 10.0 points A net positive charge Q is placed on a large, thin conducting plate of are A . In electrostatic equilibrium the charge den- sity σ on each surface and the electric field E outside the plate are 1. σ = Q A , E = σ ǫ 2. σ = Q 2 A , E = σ ǫ correct 3. σ = Q 2 A , E = 0 4. σ = 0 , E = σ ǫ 5. σ = Q 2 A , E = σ 2 ǫ fierro (jmf2547) – HW 05 – berk – (60290) 2 Explanation: 004 10.0 points A nonconducting plate with infinite dimen- sions carries a uniform surface charge density of 4 . 38 μ C / cm 2 ....
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303L-HW5 - fierro(jmf2547 – HW 05 – berk –(60290 1...

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