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ohw17-solutions - Reilly(mar3978 ohw17 turner(56725 This...

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Reilly (mar3978) – ohw17 – turner – (56725) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points What speed would a proton need to achieve in order to circle Earth 1630 km above the magnetic equator, where the Earth’s mag- netic field is directed on a line between mag- netic north and south and has an intensity of 4 × 10 8 T? The mass of a proton is 1 . 673 × 10 27 kg. Correct answer: 3 . 0642 × 10 7 m / s. Explanation: Let : h = 1630 km = 1 . 63 × 10 6 m , B = 4 × 10 8 T , q = 1 . 6 × 10 19 C , m = 1 . 673 × 10 27 kg , and r E = 6 . 38 × 10 6 m . The gravitational force is small enough to be ignored, so F c = F magnetic m v 2 h + r E = q v B Thus v = ( h + r E ) q B m = ( 1 . 63 × 10 6 m + 6 . 38 × 10 6 m ) × ( 1 . 6 × 10 19 C ) ( 4 × 10 8 T ) 1 . 673 × 10 27 kg = 3 . 0642 × 10 7 m / s . 002 10.0 points A long straight wire 1 lies along the x -axis. A long straight wire 2 lies along the y -axis so as to pass very near, but not quite touch wire 1 at the origin. If both wires are free to move, what hap- pens when currents are sent simultaneously in the + x direction through wire 1 and in the + y direction through wire 2? Note that “clock- wise around origin” refers to an observer look- ing down on an xy plane in which + x is to the right and + y upward. 1. 1 accelerates in the + y direction, 2 in the + x direction. 2. 1 accelerates in the + y direction, 2 in the - x direction. 3. 1 accelerates in the y direction, 2 in the - x direction. 4. Both wires rotate clockwise around the origin. 5. 1 rotates counterclockwise, 2 clockwise around the origin. correct 6. Neither wire moves. 7. 1 accelerates in the y direction, 2 in the + x direction. 8. 1 rotates clockwise, 2 counterclockwise around the origin. 9. Both wires rotate counterclockwise around the origin. 10. Both wires accelerate along the direction of current flow. Explanation: After the currents are turned on, each wire creates a magnetic field which applies a mag- netic force on the other wire. Consider the force on wire 1 first. According to the right- hand rule, the magnetic field from wire 2 goes into the xy plane on the right side while out of the plane on the left side. Consequently, the right half of wire 1 will have a upward force while the left half will have a downward force causing wire 1 to rotate counterclock- wise. Similarly, we find that wire 2 will rotate clockwise. 003 (part 1 of 2) 10.0 points
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Reilly (mar3978) – ohw17 – turner – (56725) 2 A rod of mass 0 . 84 kg and radius 0 . 063 m rests on two parallel rails that are 0 . 19 m apart and 0 . 64 m long. The rod carries a current of 57 A (in the direction shown) and rolls along the rails without slipping.
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