HW24Sol - Platt, David Homework 24 Due: Nov 4 2005, 4:00 am...

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Unformatted text preview: Platt, David Homework 24 Due: Nov 4 2005, 4:00 am Inst: Ken Shih 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A long cylindrical wire of radius 18 cm carries a current of 84 A uniformly distributed over its cross-sectional area. The permeability of free space is 4 10- 7 T m / A. Find the magnetic energy per unit length within the wire. Correct answer: 0 . 0001764 J / m. Explanation: r a dr Let : a = 18 cm , I = 84 A , and = 4 10- 7 T m / A . Use Amperes law, the magnetic field inside the wire at a distance r < a from its center is B = 2 r I C = 2 r r 2 a 2 I = r I 2 a 2 . The magnetic energy within the cylindrical annulus is d U m = B 2 2 V annulus = B 2 2 2 r dr = B 2 r dr = r I 2 a 2 2 r dr = 4 I 2 r 3 dr a 4 . Thus the magnetic energy per unit length within the wire is U m = Z a d U m = 4 I 2 a 4 Z a r 3 dr = 4 I 2 a 4 a 4 4 = 4 I...
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HW24Sol - Platt, David Homework 24 Due: Nov 4 2005, 4:00 am...

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