HW 7 solution

HW 7 solution - song(shs546 – Homework 7 – weathers...

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Unformatted text preview: song (shs546) – Homework 7 – weathers – (22202) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Two conductors insulated from each other are charged by transferring electrons from one conductor to the other. After 1 . 386 × 10 14 have been transferred, the potential difference between the conductors is 16 . 1 V. The charge on an electron is- 1 . 60218 × 10 − 19 C . What is the capacitance of the system? Correct answer: 1 . 37926 × 10 − 6 F. Explanation: Let : e =- 1 . 60218 × 10 − 19 C , N = 1 . 386 × 10 14 electrons , and V = 16 . 1 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 . 386 × 10 14 ) (- 1 . 60218 × 10 − 19 C) 16 . 1 V = 1 . 37926 × 10 − 6 F . 002 10.0 points A spherical capacitor consists of a conducting ball of radius 9 cm that is centered inside a grounded conducting spherical shell of inner radius 12 cm. What charge is required to achieve a potential of 1023 V on the ball of ra- dius 9 cm? The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . Correct answer: 4 . 09767 × 10 − 8 C. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , a = 9 cm = 0 . 09 m , b = 12 cm = 0 . 12 m and V = 1023 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 . 09 m) (0 . 12 m) (1023 V) (0 . 12 m)- (0 . 09 m) = 4 . 09767 × 10 − 8 C . keywords: 003 (part 1 of 2) 10.0 points A 59 m length of coaxial cable has a solid cylindrical wire inner conductor with a di- ameter of 3 . 081 mm and carries a charge of 8 . 49 μ C. The surrounding conductor is a cylindrical shell and has an inner diameter of 9 . 228 mm and a charge of- 8 . 49 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: 2 . 99212 nF. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , Q = 8 . 49 μ C , ℓ = 59 m , a = 3 . 081 mm , and b = 9 . 228 mm ....
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HW 7 solution - song(shs546 – Homework 7 – weathers...

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