# 31 - Kapoor(mk9499 – homework31 – Turner –(60230 1...

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Unformatted text preview: Kapoor (mk9499) – homework31 – Turner – (60230) 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 0 . 3163 A current is charging a capacitor that has circular plates, 13 . 99 cm in radius. The plate separation is 4 . 55 mm. The permitivity or free space is 8 . 85 × 10- 12 and the permeability of free space is 1 . 25664 × 10- 6 T · m / A. What is the time rate of increase of electric field between the plates? Correct answer: 5 . 8126 × 10 11 V / m s. Explanation: Let : I = 0 . 3163 A , r = 13 . 99 cm = 0 . 1399 m , A = π r 2 = 0 . 0614873 m 2 , and ǫ = 8 . 85 × 10- 12 . Let Φ E be the flux of the electric field, defined as Φ E = integraldisplay vector E · d vector A . Thus d Φ E dt = d dt ( E A ) = I ǫ Time rate of increase of electric field between the plates is P = d E dt = I ǫ A = . 3163 A (8 . 85 × 10- 12 )(0 . 0614873 m 2 ) = 5 . 8126 × 10 11 V / m s . 002 (part 2 of 2) 10.0 points What is the magnetic field between the plates . 023 m from the center? Correct answer: 7 . 43398 × 10- 8 T. Explanation: Let : r = 0 . 023 m and μ = 1 . 25664 × 10- 6 T · m / A . Since contintegraldisplay vector B · dvectors = ǫ μ d dt Φ E Then magnetic field, B ,at the distance r from the center between the plates satisfies 2 π r B = ǫ μ d dt parenleftbigg Q ǫ A π r 2 parenrightbigg Hence B = μ I r 2 A = (0 . 3163 A)(0 . 023 m) 2(0 . 0614873 m 2 ) × (1 . 25664 × 10- 6 T · m / A) = 7 . 43398 × 10- 8 T . 003 10.0 points A sinusoidal voltage is applied directly across a 19 . 43 μ F capacitor. The frequency of the source is 4 . 13 kHz, and the voltage amplitude is 13 . 5 V. Find the maximum value of the displace- ment current in the capacitor. Correct answer: 6 . 8067 A. Explanation: Let : C = 19 . 43 μ F = 1 . 943 × 10- 5 F , f = 4 . 13 kHz = 4130 Hz , and V max = 13 . 5 V ....
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## This note was uploaded on 06/28/2009 for the course PHY 303L taught by Professor Turner during the Fall '08 term at University of Texas.

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31 - Kapoor(mk9499 – homework31 – Turner –(60230 1...

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