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solution_pdf12 - tovar(jdt436 homework 12 Turner(59070 This...

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tovar (jdt436) – homework 12 – Turner – (59070) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 oF 2) 10.0 points A parallel-plate capacitor oF dimensions 1 . 92 cm × 3 . 36 cm is separated by a 0 . 8 mm thickness oF paper. ±ind the capacitance oF this device. The dielectric constant κ For paper is 3.7. Correct answer: 26 . 4181 p±. Explanation: Let : κ = 3 . 7 , d = 0 . 8 mm = 0 . 0008 m , and A = 1 . 92 cm × 3 . 36 cm = 0 . 00064512 m 2 . We apply the equation For the capacitance oF a parallel-plate capacitor and fnd C = κǫ 0 A d = (3 . 7) (8 . 85419 × 10 12 C 2 / N · m 2 ) × p 0 . 00064512 m 2 0 . 0008 m P 1 × 10 12 1 ± = 26 . 4181 p± . 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 . 338151 μ c. Explanation: Let : E max = 1 . 6 × 10 7 V / m . Since the thickness oF the paper is 0 . 0008 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 = (26 . 4181 p±)(12800 V) · 1 × 10 12 ± 1 p± · 1 × 10 6 μ C 1 C = 0 . 338151 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 infnite radius. 1. U = Q 2 8 π ǫ 0 a 2 2. U = Q 2 π 8 ǫ 0 a 3. U = Q 2 4 π ǫ 0 a 4. U = Q 8 π ǫ 0 a 5. U = Q 2 a 4 π ǫ 0 6. U = Q 2 8 π ǫ 0 a correct 7. U = Q 2 16 π ǫ 0 a 8. U = Q 2 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 fnd 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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tovar (jdt436) – homework 12 – Turner – (59070) 2 004 (part 2 of 4) 10.0 points Find the energy stored in a capacitor of charge Q ±lled with dielectric, use C κ = κC .
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