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Unformatted text preview: Flores, Michael Homework 9 Due: Mar 29 2004, 4:00 am Inst: Sonia Paban 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before making your selection. The due time is Central time. 001 (part 1 of 1) 10 points The recent discovery of high temperature superconductors with negligible resistance has raised many possibilities for technological applications (magnetically levitated trains, zero-dissipation power transmission lines, in- credibly strong refrigerator magnets, etc.) However, these materials lose their supercon- ductivity if they are subjected to excessive magnetic fields. This limits the amount of current that a superconductor can carry, since the current results in a magnetic field at the surface of the wire. Calculate this critical current for a d = 3 . 81 mm diameter superconducting wire if the superconductivity is destroyed when the surface magnetic field exceeds B = 0 . 0182 T. Given = 1 . 25664 10- 6 N / A 2 . Correct answer: 173 . 355 A. Explanation: Solution: This problem can be solved with Amperes law, I ~ B d~s = I Choose the integration path to be a loop around the surface. This gives us B ( d ) = I where d is the diameter. Or, I = B d = (0 . 0182 T)(0 . 00381 m) 1 . 25664 10- 6 N / A 2 = 173 . 355 A 002 (part 1 of 1) 10 points An infinitely long straight wire carrying a current I 1 = 73 . 6 A is partially surrounded by a loop as in figure. The loop has a length L = 22 . 7 cm, a radius R = 21 . 3 cm, and carries a current I 2 = 21 . 2 A. The axis of the loop coincides with the wire. R L I 1 I 2 Calculate the force exerted on the loop. Correct answer: 665 . 15 N. Explanation: The central wire creates field ~ B = I 1 2 R counterclockwise . The curved portions of the loop feels zero force since ~ l ~ B = 0 there. The straight portions both feel I 2 ~ l ~ B forces to the right, amounting to ~ F = I 2 2 L I 1 2 R = I 1 I 2 L R to the right k ~ F k = (73 . 6 A)(21 . 2 A)(0 . 227 m) (21 . 3 cm) = 665 . 15 N . 003 (part 1 of 2) 10 points A superconducting solenoid is to generate a magneticfieldof14 . 9T. Thesolenoidwinding has 1290 turns per meter. What is the required current? Correct answer: 9191 . 51 A. Explanation: Magnetic field at the center of solenoid is B = N I l = nI , then I = B l N Flores, Michael Homework 9 Due: Mar 29 2004, 4:00 am Inst: Sonia Paban 2 = (14 . 9 T) (1290) = 9191 . 51 A . 004 (part 2 of 2) 0 points What force per unit length is exerted on the windings by this magnetic field? Correct answer: 136953 N / m. Explanation: Force per unit length is F l = I B = (9191 . 51 A)(14 . 9 T) = (136953 N / m) radially outward ....
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This note was uploaded on 02/18/2010 for the course PHYS 303l taught by Professor Panab during the Spring '04 term at North Texas.
- Spring '04