Homework 9 Solutions

52 we find n the number of turns of the solenoid from

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Unformatted text preview: ⎟ 2prdr = 0 0 . 3a ⎝a⎠ (a) At r = 0, B = 0 . (b) At r = a / 2 , we have B (r ) = μ0 J 0 r 2 3a = (4π ×10−7 T ⋅ m/A)(310A/m 2 )(3.1×10−3 m / 2) 2 = 1.0 ×10−7 T. 3(3.1×10−3 m) (c) At r = a, B (r = a) = μ 0 J 0 a (4π×10−7 T ⋅ m/A)(310A/m 2 )(3.1×10−3 m) 3 = 3 = 4.0 ×10−7 T. 48. (a) The field at the center of the pipe (point C) is due to the wire alone, with a magnitude of μi μi BC = 0 wire = 0 wire . 2π ( 3R ) 6π R For the wire we have BP, wire > BC, wire. Thus, for BP = BC = BC, wire, iwire must be into the page: 1144 CHAPTER 29 BP = BP ,wire − BP ,pipe = μ0iwire μ0i − . 2π R 2π ( 2 R ) Setting BC = –BP we obtain iwire = 3i/8 = 3(8.00 ×10−3 A) / 8 = 3.00 ×10−3 A . (b) The direction is into the page. 49. (a) We use Eq. 29-24. The inner radius is r = 15.0 cm, so the field there is B= −7 μ0iN ( 4π×10 T ⋅ m/A ) ( 0.800 A ) ( 500 ) = = 5.33×10−4 T. 2π r 2π ( 0.150 m ) (b) The outer radius is r = 20.0 cm. The field there is −7 μ0iN ( 4π ×10 T ⋅ m/A ) ( 0.800 A ) ( 500 ) = = 4.00 ×10−4 T. B= 2π r 2π ( 0.200m ) 50. It is possible (though tedious) to use Eq. 29-26 and evaluate the contributions (with the intent to sum them) of all 1200 loops to the field at, say, the center of the solenoid. This would make use of all the information given in the problem statement, but this is not the method that the student is expected to use here. Instead, Eq. 29-23 for the ideal solenoid (which does not make use of the coil radius) is the preferred method: B = μ 0in = μ 0i where i = 3.60 A, FG N IJ HK = 0.950 m, and N = 1200. This yields B = 0.00571 T. 51. It is possible (though tedious) to use Eq. 29-26 and evaluate the contributions (with the intent to sum them) of all 200 loops to the field at, say, the center of the solenoid. This would make use of all the information given in the problem statement, but this is not the method that the student is expected to use here. Instead, Eq. 29-23 for the ideal sole...
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This document was uploaded on 02/26/2014 for the course PHYS 2b at UCSD.

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