solutions 7 - Patel, Kinal Homework 7 Due: Feb 15 2008,...

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Patel, Kinal – Homework 7 – Due: Feb 15 2008, 7:00 pm – Inst: Weathers 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 1) 10 points Two conductors insulated ±rom each other are charged by trans±erring electrons ±rom one conductor to the other. A±ter 2 . 1962 × 10 14 have been trans±erred, the potential di²erence between the conductors is 14 . 2 V. The charge on an electron is - 1 . 60218 × 10 - 19 C . What is the capacitance o± the system? Correct answer: 2 . 47796 × 10 - 6 F. Explanation: Let : e = - 1 . 60218 × 10 - 19 C , N = 2 . 1962 × 10 14 electrons , and V = 14 . 2 V . One conductor gains a charge o± Q = - N e while the other gains a charge o± - Q. The capacitance o± the system is C = q V = - N e V = - (2 . 1962 × 10 14 ) ( - 1 . 60218 × 10 - 19 C) 14 . 2 V = 2 . 47796 × 10 - 6 F . keywords: 002 (part 1 o± 1) 10 points A spherical capacitor consists o± a conducting ball o± radius 12 cm that is centered inside a grounded conducting spherical shell o± inner radius 14 cm. The Coulomb constant is 8 . 98755 × 10 9 N m 2 / C 2 . What charge is required to achieve a poten- tial o± 1378 V on the ball o± radius 12 cm? Correct answer: 1 . 28791 × 10 - 7 C. Explanation: Let : k e = 8 . 98755 × 10 9 N m 2 / C 2 , a = 12 cm = 0 . 12 m , b = 14 cm = 0 . 14 m and V = 1378 V . The capacitance o± a spherical capacitor is given by C = ab k e ( b - a ) . The charge required to achieve a potential di²erence V between the shell and the ball is given by Q = C V = 1 k e abV ( b - a ) = 1 (8 . 98755 × 10 9 N m 2 / C 2 ) × (0 . 12 m) (0 . 14 m) (1378 V) (0 . 14 m) - (0 . 12 m) = 1 . 28791 × 10 - 7 C . keywords: 003 (part 1 o± 2) 10 points A 29 m length o± coaxial cable has a solid cylindrical wire inner conductor with a di- ameter o± 3 . 144 mm and carries a charge o± 11 . 61 μ C. The surrounding conductor is a cylindrical shell and has an inner diameter o± 8 . 436 mm and a charge o± - 11 . 61 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 o± this cable? Correct answer: 1 . 63457 nF. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , Q = 11 . 61 μ C , = 29 m , a = 3 . 144 mm , and b = 8 . 436 mm . The charge per unit length is λ Q . V = - Z b a ~ E · d~s
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Patel, Kinal – Homework 7 – Due: Feb 15 2008, 7:00 pm – Inst: Weathers 2 = - 2 k e λ Z b a dr r = - 2 k e Q ln µ b a . The capacitance of a cylindrical capacitor is given by C Q V = 2 k e 1 ln µ b a = 29 m 2 (8 . 98755 × 10 9 N · m 2 / C 2 ) × 1 ln µ 8 . 436 mm 3 . 144 mm · µ 1 × 10 9 nF 1 F = 1 . 63457 nF 004 (part 2 of 2) 10 points What is the potential di±erence between the two conductors? Correct answer: 7
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solutions 7 - Patel, Kinal Homework 7 Due: Feb 15 2008,...

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