hw15 - solenoid with radius 2.4 cm length 30 cm and 40,000...

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Physics 21 Fall, 2008 Solution to HW-15 28-39 A long, straight, cylindrical wire of radius R carries a current uniformly distributed over its cross section. At what location is the magnetic Feld produced by this current equal to half of its largest value? Consider points (a) inside and (b) outside the wire. Outside the wire, the Amperian loop of radius r will en- close all the current in the wire, and the Feld will be µ 0 I/ 2 πr . The half max point occurs at r =2 R . 28.41 A solenoid is designed to produce a magnetic Feld of 4 . 00 × 10 - 2 T at its center. It has a radius of 1.50 cm and a length of 35.0 cm, and the wire can carry a maximum current of 12.0 A. (a) What minimum number of turns per unit length must the solenoid have? (b) What total length of wire is required? 28-43 A magnetic Feld of 37.2 T has been achieved at the MIT ±rancis Bitter National Magnetic Laboratory. ±ind the current needed to achieve such a Feld (a) 2.2 cm from a long, straight wire, (b) at the center of a circular coil of radius 42 cm that has 100 turns, and (c) near the center of a
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Unformatted text preview: solenoid with radius 2.4 cm, length 30 cm, and 40,000 turns. 28.44 The toroidal solenoid shown in the Fgure has inner radius 13.4 cm and outer radius 19.2 cm. The solenoid has 250 turns and carries a current of 9.20 A. (a) What is the magnitude of the magnetic Feld at 10.9 cm from the center of the torus? (b) What is the magnitude of the magnetic Feld at 16.3 cm from the center of the torus? (c) What is the magnitude of the magnetic Feld at 21.4 cm from the center of the torus? 28.47 A toroidal solenoid with 500 turns is wound on a ring with a mean radius of 3.00 cm. (a) ±ind the current in the winding that is required to set up a magnetic Feld of 0.370 T in the ring if the ring is made of annealed iron K m = 1400. (b) ±ind the current in the winding that is required to set up a magnetic Feld of 0.370 T in the ring if the ring is made of silicon steel K m = 5200. October 6, 2008...
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