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# HW 12 - terry(ect328 – homework 12 – Turner –(59130 1...

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Unformatted text preview: terry (ect328) – homework 12 – Turner – (59130) 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 2 . 55 cm × 4 . 99 cm is separated by a 1 . 55 mm thickness of paper. Find the capacitance of this device. The dielectric constant κ for paper is 3.7. Correct answer: 26 . 8943 pF. Explanation: Let : κ = 3 . 7 , d = 1 . 55 mm = 0 . 00155 m , and A = 2 . 55 cm × 4 . 99 cm = 0 . 00127245 m 2 . We apply the equation for the capacitance of a parallel-plate capacitor and find C = κǫ A d = (3 . 7) (8 . 85419 × 10 − 12 C 2 / N · m 2 ) × parenleftbigg . 00127245 m 2 . 00155 m parenrightbigg 1 × 10 12 pF 1 F = 26 . 8943 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 . 666977 μ c. Explanation: Let : E max = 1 . 6 × 10 7 V / m . Since the thickness of the paper is 0 . 00155 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 . 8943 pF)(24800 V) · 1 × 10 − 12 F 1 pF · 1 × 10 6 μ C 1 C = . 666977 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 2. U = Q 2 π 8 ǫ a 3. U = Q 8 π ǫ a 4. U = Q 2 4 π ǫ a 5. U = Q 2 8 π ǫ a 2 6. U = Q 2 8 π ǫ a correct 7. U = Q 2 a 4 π ǫ 8. U = Q 2 16 π ǫ a Explanation: The capacitance formula for a spherical ca- pacitor of inner radius a and outer radius b is C = ab 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 a....
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HW 12 - terry(ect328 – homework 12 – Turner –(59130 1...

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