homework 09a-solutions.pdf - agha(msa2448 homework 09a...

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agha (msa2448) – homework 09a – turner – (90130) 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(part1of2)10.0points The plates of a parallel-plate capacitor of di- mensions 2 . 46 cm × 4 . 12 cm are separated by a 0 . 82 mm thickness of paper. Find the capacitance of this device. The dielectric constant κ for paper is 3.7. Correct answer: 40 . 492 pF. Explanation: Let : κ = 3 . 7 , d = 0 . 82 mm = 0 . 00082 m , and A = 2 . 46 cm × 4 . 12 cm = 0 . 00101352 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 . 00101352 m 2 0 . 00082 m parenrightbigg 1 × 10 12 pF 1 F = 40 . 492 pF . 002(part2of2)10.0points What is the maximum charge that can be placed on the capacitor? The dielectric strength of paper is 1 . 6 × 10 7 V / m. Correct answer: 0 . 531255 μ c. Explanation: Let : E max = 1 . 6 × 10 7 V / m . Since the thickness of the paper is 0 . 00082 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 = (40 . 492 pF)(13120 V) · 1 × 10 12 F 1 pF · 1 × 10 6 μ C 1 C = 0 . 531255 μ c . 003(part1of4)10.0points 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 8 π ǫ 0 a 2 2. U = Q 2 8 π ǫ 0 a correct 3. U = Q 2 16 π ǫ 0 a 4. U = Q 2 4 π ǫ 0 a 5. U = Q 2 π 8 ǫ 0 a 6. U = Q 8 π ǫ 0 a 7. U = Q 2 a 8. U = Q 2 a 4 π ǫ 0 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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agha (msa2448) – homework 09a – turner – (90130) 2 004(part2of4)10.0points Find the energy stored in a capacitor of charge Q filled with dielectric, use C κ = κ C .
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