Homework05

Homework05 - johnson(rj6247 hw 5 Opyrchal(121014 This...

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johnson (rj6247) – hw 5 – Opyrchal – (121014) 1 This print-out should have 17 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 75 m length oF coaxial cable has a solid cylindrical wire inner conductor with a di- ameter oF 3 . 142 mm and carries a charge oF 7 . 08 μ C. The surrounding conductor is a cylindrical shell and has an inner diameter oF 7 . 928 mm and a charge oF - 7 . 08 μ C. Assume the region between the conductors is air. The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . What is the capacitance oF this cable? Correct answer: 4 . 50811 n±. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , Q = 7 . 08 μ C , = 75 m , a = 3 . 142 mm , and b = 7 . 928 mm . The charge per unit length is λ Q . V = - i b a v E · dvs = - 2 k e λ i b a dr r = - 2 k e Q ln p b a P . The capacitance oF a cylindrical capacitor is given by C Q V = 2 k e 1 ln p b a P = 75 m 2 (8 . 98755 × 10 9 N · m 2 / C 2 ) × 1 ln p 7 . 928 mm 3 . 142 mm P · p 1 × 10 9 1 ± P = 4 . 50811 n± 002 (part 2 oF 2) 10.0 points What is the potential di²erence between the two conductors? Correct answer: 1 . 5705 kV. Explanation: ThereFore V = Q C = 7 . 08 μ C 4 . 50811 n± p 1 × 10 9 1 ± P × p 1 C 1 × 10 6 μ C Pp 1 kV 1000 V P = 1 . 5705 kV 003 10.0 points Two conductors insulated From each other are charged by transFerring electrons From one conductor to the other. AFter 2 . 621 × 10 13 have been transFerred, the potential di²erence between the conductors is 14 . 6 V. The charge on an electron is - 1 . 60218 × 10 19 C . What is the capacitance oF the system? Correct answer: 2 . 87624 × 10 7 ±. Explanation: Let : e = - 1 . 60218 × 10 19 C , N = 2 . 621 × 10 13 electrons , and V = 14 . 6 V . One conductor gains a charge oF Q = - N e while the other gains a charge oF - Q. The capacitance oF the system is C = q V = - N e V = - (2 . 621 × 10 13 ) ( - 1 . 60218 × 10 19 C) 14 . 6 V = 2 . 87624 × 10 7 ± .
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johnson (rj6247) – hw 5 – Opyrchal – (121014) 2 004 (part 1 of 2) 10.0 points The potential diFerence between a pair of oppositely charged parallel plates is 386 V. a) If the spacing between the plates is dou- bled without altering the charge on the plates, what is the new potential diFerence between the plates? Correct answer: 772 V. Explanation: Let : d 2 = 2 d 1 and Δ V 1 = 386 V . The charge remains the same, so Q = C 1 Δ V 1 = C 2 Δ V 2 ε 0 A d 1 Δ V 1 = ε 0 A d 2 Δ V 2 Δ V 1 d 1 = Δ V 2 d 2 Δ V 1 d 1 = Δ V 2 2 d 1 Δ V 2 = 2Δ V 1 = 2(386 V) = 772 V .
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Homework05 - johnson(rj6247 hw 5 Opyrchal(121014 This...

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