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Homework_07 - Nguyen Thanh Homework 7 Due 7:00 pm Inst...

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Nguyen, Thanh – 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 – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Two conductors insulated from each other are charged by transferring electrons from one conductor to the other. After 1 . 401 × 10 13 have been transferred, the potential difference between the conductors is 16 . 3 V. The charge on an electron is - 1 . 60218 × 10 - 19 C . What is the capacitance of the system? Correct answer: 1 . 37709 × 10 - 7 F. Explanation: Let : e = - 1 . 60218 × 10 - 19 C , N = 1 . 401 × 10 13 electrons , and V = 16 . 3 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 = - (1 . 401 × 10 13 ) ( - 1 . 60218 × 10 - 19 C) 16 . 3 V = 1 . 37709 × 10 - 7 F . keywords: 002 (part 1 of 1) 10 points A spherical capacitor consists of a conducting ball of radius 4 cm that is centered inside a grounded conducting spherical shell of inner radius 8 cm. The Coulomb constant is 8 . 98755 × 10 9 N m 2 / C 2 . What charge is required to achieve a poten- tial of 876 V on the ball of radius 4 cm? Correct answer: 7 . 79745 × 10 - 9 C. Explanation: Let : k e = 8 . 98755 × 10 9 N m 2 / C 2 , a = 4 cm = 0 . 04 m , b = 8 cm = 0 . 08 m and V = 876 V . The capacitance of a spherical capacitor is given by C = a b k e ( b - a ) . The charge required to achieve a potential difference V between the shell and the ball is given by Q = C V = 1 k e a b V ( b - a ) = 1 (8 . 98755 × 10 9 N m 2 / C 2 ) × (0 . 04 m) (0 . 08 m) (876 V) (0 . 08 m) - (0 . 04 m) = 7 . 79745 × 10 - 9 C . keywords: 003 (part 1 of 2) 10 points A 20 m length of coaxial cable has a solid cylindrical wire inner conductor with a di- ameter of 1 . 192 mm and carries a charge of 7 . 31 μ C. The surrounding conductor is a cylindrical shell and has an inner diameter of 10 . 515 mm and a charge of - 7 . 31 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: 0 . 511053 nF. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , Q = 7 . 31 μ C , = 20 m , a = 1 . 192 mm , and b = 10 . 515 mm . The charge per unit length is λ Q . V = - Z b a ~ E · d~s
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Nguyen, Thanh – 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 b a . The capacitance of a cylindrical capacitor is given by C Q V = 2 k e 1 ln b a = 20 m 2 (8 . 98755 × 10 9 N · m 2 / C 2 ) × 1 ln 10 . 515 mm 1 . 192 mm · 1 × 10 9 nF 1 F = 0 . 511053 nF 004 (part 2 of 2) 10 points What is the potential difference between the two conductors? Correct answer: 14 . 3038 kV. Explanation: Therefore V = Q C = 7 . 31 μ C 0 . 511053 nF 1 × 10 9 nF 1 F × 1 C 1 × 10 6 μ C 1 kV 1000 V = 14 . 3038 kV keywords: 005 (part 1 of 1) 10 points The plates of a parallel-plate capacitor are separated by 0 . 111 mm.
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