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# hw 12 - nguyen(jmn727 homework 12 Turner(59070 This...

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nguyen (jmn727) – homework 12 – Turner – (59070) 1 This print-out should have 12 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 parallel-plate capacitor of dimensions 1 . 72 cm × 3 . 35 cm is separated by a 0 . 78 mm thickness of paper. Find the capacitance of this device. The dielectric constant κ for paper is 3.7. Correct answer: 24 . 2008 pF. Explanation: Let : κ = 3 . 7 , d = 0 . 78 mm = 0 . 00078 m , and A = 1 . 72 cm × 3 . 35 cm = 0 . 0005762 m 2 . We apply the equation for the capacitance of a parallel-plate capacitor and find C = κ ǫ 0 A d = (3 . 7) (8 . 85419 × 10 12 C 2 / N · m 2 ) × parenleftbigg 0 . 0005762 m 2 0 . 00078 m parenrightbigg 1 × 10 12 pF 1 F = 24 . 2008 pF . 002 (part 2 of 2) 10.0 points What is the maximum charge that can be placed on the capacitor? The electric strength of paper is 1 . 6 × 10 7 V / m. Correct answer: 0 . 302026 μ c. Explanation: Let : E max = 1 . 6 × 10 7 V / m . Since the thickness of the paper is 0 . 00078 m, the maximum voltage that can be applied before breakdown is V max = E max d . Hence, the maximum charge is Q max = C V max = C E max d = (24 . 2008 pF)(12480 V) · 1 × 10 12 F 1 pF · 1 × 10 6 μ C 1 C = 0 . 302026 μ c . 003 (part 1 of 4) 10.0 points Determine the total energy stored in a con- ducting sphere with charge Q . Hint: Use the capacitance formula for a spherical capacitor which consists of two spherical shells. Take the inner sphere to have a radius a and the outer shell to have an infinite radius. 1. U = Q 2 a 4 π ǫ 0 2. U = Q 2 8 π ǫ 0 a 2 3. U = Q 8 π ǫ 0 a 4. U = Q 2 π 8 ǫ 0 a 5. U = Q 2 a 6. U = Q 2 8 π ǫ 0 a correct 7. U = Q 2 4 π ǫ 0 a 8. U = Q 2 16 π ǫ 0 a Explanation: The capacitance formula for a spherical ca- pacitor of inner radius a and outer radius b is C = a b k e ( b - a ) . If we let b → ∞ , we find we can neglect a in the denominator compared to b , so C a k e = 4 π ǫ 0 a . The total energy stored is U = Q 2 2 C = Q 2 8 π ǫ 0 a .

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nguyen (jmn727) – homework 12 – Turner – (59070) 2 004 (part 2 of 4) 10.0 points Find the energy stored in a capacitor of charge Q filled with dielectric, use C κ = κ C .
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