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# HW3 - johnson(rj6247 – hw 3 – Opyrchal –(121014 1...

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Unformatted text preview: johnson (rj6247) – hw 3 – Opyrchal – (121014) 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 10.0 points An electric field of magnitude 8000 N / C and directed upward perpendicular to the Earth’s surface exists on a day when a thunderstorm is brewing. A truck that can be approximated as a rectangle 4 . 9 m by 4 . 6 m is traveling along a road that is inclined 11 ◦ relative to the ground. Determine the electric flux through the bot- tom of the truck. Correct answer: 1 . 77007 × 10 5 N · m 2 / C. Explanation: Let : E = 8000 N / C , ℓ = 4 . 9 m , w = 4 . 6 m , and θ = 11 ◦ . By Gauss’ law, Φ = vector E · vector A The flux through the bottom of the car is Φ = E A cos θ = E ℓ w cos θ = (8000 N / C) (4 . 9 m) × (4 . 6 m) cos(11 ◦ ) = 1 . 77007 × 10 5 N · m 2 / C . 002 10.0 points A nonconducting wall carries a uniform charge density of 13 . 14 μ C / cm 2 . What is the electric field 4 . 3 cm in front of the wall? Correct answer: 7 . 42022 × 10 9 N / C. Explanation: Let : σ = 13 . 14 μ C / cm 2 and r = 4 . 3 cm . The electric field of an infinite plane of surface charge density σ is E = σ 2 ǫ = 13 . 14 μ C / cm 2 2 (8 . 85419 × 10 − 12 C 2 / N · m 2 ) × parenleftbigg 1 C 10 6 μ C parenrightbigg · parenleftbigg 100 cm 1 m parenrightbigg 2 = 7 . 42022 × 10 9 N / C . 003 (part 1 of 2) 10.0 points A thin spherical shell of radius 4 . 93 m has a total charge of 8 . 11 C distributed uniformly over its surface. Let : k e = 8 . 988 × 10 9 N · m 2 / C 2 . 4 . 9 3 m vector E + + + + + + + + + + + + + + + + + + + + Find the electric field vector E 11 . 7 m from the center of the shell (outside the shell). Correct answer: 5 . 32491 × 10 8 N / C. Explanation: Let : a = 4 . 93 m , Q = 8 . 11 C , and r = 11 . 7 m . If we construct a spherical Gaussian surface of radius r > a , concentric with the shell, then the charge inside this surface is Q . Therefore the field at a point outside the shell is equiva- lent to that of a point charge Q at the center....
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HW3 - johnson(rj6247 – hw 3 – Opyrchal –(121014 1...

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