solution_pdf26 - tovar (jdt436) homework 26 Turner (59070)...

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Unformatted text preview: tovar (jdt436) homework 26 Turner (59070) 1 This print-out should have 11 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 solenoid has 133 turns of wire uniformly wrapped around an air-filled core, which has a diameter of 16 mm and a length of 8 . 6 cm. The permeability of free space is 1 . 25664 10 6 N / A 2 . Calculate the self-inductance of the solenoid. Correct answer: 5 . 1969 10 5 H. Explanation: Let : N = 133 , D = 16 mm = 0 . 016 m , = 8 . 6 cm = 0 . 086 m , and = 1 . 25664 10 6 N / A 2 . The self-inductance of a solenoid is given by L 1 = N I , where is the total flux inside the solenoid and I is the current in the wire wrapped around the solenoid. By Amperes Law, the magnetic field in the solenoid is B = N I , where = is the magnetic permeability of the air core which is the same as free space. The magnetic flux in the solenoid is = B A = B D 2 4 . Using the above expressions for and B , we obtain for the inductance of the solenoid L 1 = N B A I = N 2 D 2 4 = (1 . 25664 10 6 N / A 2 ) (133) 2 (0 . 016 m) 2 4 (0 . 086 m) = 5 . 1969 10 5 H . 002 (part 2 of 2) 10.0 points The core is replaced with a soft iron rod that has the same dimensions, but a magnetic per- meability of 800 . What is the new inductance? Correct answer: 0 . 0415752 H. Explanation: Let : = 800 . L 2 = N 2 D 2 4 = L 1 = 800(5 . 1969 10 5 H) = . 0415752 H . 003 (part 1 of 2) 10.0 points The current in a 72 mH inductor changes with time as I = b t 2- a t . With a = 7 A / s and b = 5 A / s 2 , find the magnitude of the induced emf , |E| , at t = 0 . 4 s. Correct answer: 0 . 216 V. Explanation: Let : L = 72 mH = 0 . 072 H , b = 5 A / s 2 , a = 7 A / s , and t = 0 . 4 s . From Faradays Law, the induced emf E is proportional to the rate of change of the magnetic flux, which in turn is proportional to the rate of change of the current. This is expressed as E = L d I dt = L d dt ( b t 2- a t ) = L (2 b t- a ) tovar (jdt436) homework 26 Turner (59070) 2 At 0 . 4 s ,the magnitude of the induced...
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This note was uploaded on 12/11/2009 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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solution_pdf26 - tovar (jdt436) homework 26 Turner (59070)...

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