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Spring 11 Phys 121 - HW 12

# Spring 11 Phys 121 - HW 12 - dzifanu(sd26397 – hw 12 –...

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Unformatted text preview: dzifanu (sd26397) – hw 12 – opyrchal – (121102) 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 10.0 points A coiled telephone cord forms a spiral with 81 . 6 turns, a diameter of 2 . 04 cm, and an unstretched length of 33 . 7 cm. The permeability of free space is 1 . 25664 × 10 − 6 T · m / A. Determine the self-inductance of one con- ductor in the unstretched cord. Correct answer: 8 . 11541 μ H. Explanation: Let : μ = 1 . 25664 × 10 − 6 T · m / A , N = 81 . 6 , r = 1 . 02 cm = 0 . 0102 m , and ℓ = 33 . 7 cm = 0 . 337 m . Treating the coiled telephone cord as a solenoid, the self-inductance is L = μ N 2 A ℓ = μ N 2 π r 2 ℓ = ( 1 . 25664 × 10 − 6 T · m / A ) × (81 . 6) 2 π (0 . 0102 m) 2 . 337 m · 10 6 μ H H = 8 . 11541 μ H . 002 10.0 points An emf of 50 . 5 mV is induced in a 413-turn coil when the current is changing at a rate of 11 . 9 A / s. What is the magnetic flux through each turn of the coil at an instant when the current is 3 . 28 A? Correct answer: 3 . 3703 × 10 − 5 Wb. Explanation: Let : E = 50 . 5 mV = 0 . 0505 V , N = 413 , I = 3 . 28 A , and dI dt = 11 . 9 A / s . From Faraday’s Law E =- N d Φ dt =- L d I dt |E| = L d I dt L = |E| d I dt = . 0505 V 11 . 9 A / s = 0 . 0042437 H . At the instant where the current is 3 . 28 A , the flux through each turn is Φ = L I N = (0 . 0042437 H) (3 . 28 A) 413 = 3 . 3703 × 10 − 5 Wb . 003 10.0 points A solenoid inductor is 30 cm long and has a cross-sectional area of 5 cm 2 . When the current through the solenoid decreases at a rate of 0 . 625 A / s, the induced emf is 270 μ V. The permeability of free space is 1 . 25664 × 10 − 6 N / A 2 . Find the number of turns per meter of the solenoid. Correct answer: 1513 . 88 m − 1 . Explanation: Let : ℓ = 30 cm = 0 . 3 m , A = 5 cm 2 = 0 . 0005 m 2 , E = 270 μ V = 0 . 00027 V , r = 0 . 625 A / s , and μ = 1 . 25664 × 10 − 6 N / A 2 . The induced emf in the solenoid is ε =- L d I dt . dzifanu (sd26397) – hw 12 – opyrchal – (121102) 2 The self-inductance of a solenoid is L = μ N 2 A ℓ ....
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Spring 11 Phys 121 - HW 12 - dzifanu(sd26397 – hw 12 –...

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