HW5 - zhou(cz3574 – HW5 – mackie –(10621 1 This...

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Unformatted text preview: zhou (cz3574) – HW5 – mackie – (10621) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. NOTE TUES DEADLINE! 001 10.0 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 7 cm. What charge is required to achieve a potential of 1320 V on the ball of ra- dius 4 cm? The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . Correct answer: 1 . 37078 × 10 − 8 C. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , a = 4 cm = 0 . 04 m , b = 7 cm = 0 . 07 m and V = 1320 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 . 07 m) (1320 V) (0 . 07 m)- (0 . 04 m) = 1 . 37078 × 10 − 8 C . keywords: 002 10.0 points An air-filled cylindrical capacitor has a capac- itance of 13 pF and is 9 . 4 cm in length. The coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . If the radius of the outside conductor is 1 . 3 cm, what is the required radius of the inner conductor? Correct answer: 0 . 869444 cm. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , ℓ = 9 . 4 cm = 0 . 094 m , b = 1 . 3 cm , and C = 13 pF = 1 . 3 × 10 − 11 F . The capacitance of a cylindrical capacitor is given by C = ℓ 2 k e ln b a where a and b are the inner and outer radii, respectively. Solving for a , we obtain a = b e − ℓ/ (2 k e C ) = (1 . 3 cm) e − (0 . 094 m) / [2 k e (1 . 3 × 10- 11 F)] = . 869444 cm . 003 10.0 points A 10 . 2 V battery is connected to a 6 . 9 pF parallel-plate capacitor. What is the magnitude of the charge on each plate? Correct answer: 7 . 038 × 10 − 11 C. Explanation: Let : Δ V = 10 . 2 V and C = 6 . 9 pF . The capacitance is C = Q Δ V Q = C Δ V = (6 . 9 × 10 − 12 F) (10 . 2 V) = 7 . 038 × 10 − 11 C . zhou (cz3574) – HW5 – mackie – (10621) 2 004 10.0 points A parallel-plate capacitor is made by placing polyethylene ( κ = 2 . 3) between two sheets of aluminum foil. The area of each sheet of aluminum foil is 450 cm 2 , and the thickness of the polyethylene is 0 . 3 mm. The permittivity of free space is 8 . 85 × 10 − 12 C 2 / N · m 2 . Find the capacitance. Correct answer: 3 . 05325 nF. Explanation: Let : κ = 2 . 3 , ǫ = 8 . 85 × 10 − 12 C 2 / N · m 2 , A = 450 cm 2 = 0 . 045 m 2 , and d = 0 . 3 mm = 0 . 0003 m . The capacitance is C = κ ǫ A d = 2 . 3(8 . 85 × 10 − 12 C 2 / N · m 2 ) (0 . 045 m 2 ) . 0003 m × 10 9 nF F = 3 . 05325 nF ....
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HW5 - zhou(cz3574 – HW5 – mackie –(10621 1 This...

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