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oldhw 33 - nguyen(jmn727 oldhomework 33 Turner(59070 This...

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nguyen (jmn727) – oldhomework 33 – 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 0 . 3071 A current is charging a capacitor that has circular plates, 11 . 14 cm in radius. The plate separation is 3 . 49 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: 8 . 90054 × 10 11 V / m s. Explanation: Let : I = 0 . 3071 A , r = 11 . 14 cm = 0 . 1114 m , A = π r 2 = 0 . 038987 m 2 , and ǫ 0 = 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 0 Time rate of increase of electric field between the plates is P = d E dt = I ǫ 0 A = 0 . 3071 A (8 . 85 × 10 - 12 )(0 . 038987 m 2 ) = 8 . 90054 × 10 11 V / m s . 002 (part 2 of 2) 10.0 points What is the magnetic field between the plates 0 . 0595 m from the center? Correct answer: 2 . 9448 × 10 - 7 T. Explanation: Let : r = 0 . 0595 m and μ 0 = 1 . 25664 × 10 - 6 T · m / A . Since contintegraldisplay vector B · dvectors = ǫ 0 μ 0 d dt Φ E Then magnetic field, B ,at the distance r from the center between the plates satisfies 2 π r B = ǫ 0 μ 0 d dt parenleftbigg Q ǫ 0 A π r 2 parenrightbigg Hence B = μ 0 I r 2 A = (0 . 3071 A)(0 . 0595 m) 2(0 . 038987 m 2 ) × (1 . 25664 × 10 - 6 T · m / A) = 2 . 9448 × 10 - 7 T . 003 10.0 points A sinusoidal voltage is applied directly across a 19 . 23 μ F capacitor. The frequency of the source is 5 . 2 kHz, and the voltage amplitude is 41 . 4 V. Find the maximum value of the displace- ment current in the capacitor. Correct answer: 26 . 0113 A. Explanation: Let : C = 19 . 23 μ F = 1 . 923 × 10 - 5 F , f = 5 . 2 kHz = 5200 Hz , and V max = 41 . 4 V . The angular frequency of the source is ω = 2 π f = 2 π (5200 Hz) = 32672 . 6 s - 1 . The voltage across the capacitor as a function of t is V = V max sin( ω t ) = (41 . 4 V) sin bracketleftbig (32672 . 6 s - 1 ) t bracketrightbig .
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nguyen (jmn727) – oldhomework 33 – Turner – (59070) 2 Now we can find the charge on the capacitor, Q = CV , and to calculate the displacement current I d
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