121HW5 - lew(dl9564 hw 5 Opyrchal(121006 This print-out...

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lew (dl9564) – hw 5 – Opyrchal – (121006) 1 This print-out should have 17 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 31 m length of coaxial cable has a solid cylindrical wire inner conductor with a di- ameter of 2 . 042 mm and carries a charge of 7 . 32 μ C. The surrounding conductor is a cylindrical shell and has an inner diameter of 6 . 748 mm and a charge of - 7 . 32 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: 1 . 4428 nF. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , Q = 7 . 32 μ C , = 31 m , a = 2 . 042 mm , and b = 6 . 748 mm . The charge per unit length is λ Q . V = - integraldisplay b a vector E · dvectors = - 2 k e λ integraldisplay b a dr r = - 2 k e Q ln parenleftbigg b a parenrightbigg . The capacitance of a cylindrical capacitor is given by C Q V = 2 k e 1 ln parenleftbigg b a parenrightbigg = 31 m 2 (8 . 98755 × 10 9 N · m 2 / C 2 ) × 1 ln parenleftbigg 6 . 748 mm 2 . 042 mm parenrightbigg · parenleftbigg 1 × 10 9 nF 1 F parenrightbigg = 1 . 4428 nF 002 (part 2 of 2) 10.0 points What is the potential difference between the two conductors? Correct answer: 5 . 07345 kV. Explanation: Therefore V = Q C = 7 . 32 μ C 1 . 4428 nF parenleftbigg 1 × 10 9 nF 1 F parenrightbigg × parenleftbigg 1 C 1 × 10 6 μ C parenrightbigg parenleftbigg 1 kV 1000 V parenrightbigg = 5 . 07345 kV 003 10.0 points Two conductors insulated from each other are charged by transferring electrons from one conductor to the other. After 9 . 852 × 10 13 have been transferred, the potential difference between the conductors is 11 . 7 V. The charge on an electron is - 1 . 60218 × 10 19 C . What is the capacitance of the system? Correct answer: 1 . 34911 × 10 6 F. Explanation: Let : e = - 1 . 60218 × 10 19 C , N = 9 . 852 × 10 13 electrons , and V = 11 . 7 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 = - (9 . 852 × 10 13 ) ( - 1 . 60218 × 10 19 C) 11 . 7 V = 1 . 34911 × 10 6 F .
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lew (dl9564) – hw 5 – Opyrchal – (121006) 2 004 (part 1 of 2) 10.0 points The potential difference between a pair of oppositely charged parallel plates is 351 V. a) If the spacing between the plates is dou- bled without altering the charge on the plates, what is the new potential difference between the plates?
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