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# hw10 - magnetic ﬁeld is 0 3 × 10-4 T at the height of...

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Electricity and Magnetism I (P331) Homework 8 Due: Friday, December 11, 4:00 PM The final exam will be Friday, December 18 from 12:30 PM - 2:30 PM in Swain West 219. 1. In 1996 astronauts on the space shuttle Columbia did an interesting experiment to test an idea for generating electric power in satellites in orbit around Earth using a conducting tether. Columbia deployed a satellite attached to the space shuttle by a 20-km long tether. Motion of the tether through the Earth’s magnetic field would generate a voltage drop across the tether. (In vacuum, charge would build up on the ends, but in the ionosphere current would flow, the return current being in the plasma.) Assume the tether is a straight wire, held taut by the shuttle and satellite at its ends. The whole system revolves around the Earth with a speed 8 km/s. Assume for simplicity that the wire direction , velocity v , and the Earth’s magnetic field B are all mutually orthogonal.
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Unformatted text preview: magnetic ﬁeld is 0 . 3 × 10-4 T at the height of the satellite. Calculate the voltage diﬀerence between the ends of the wire. (In the NASA experiment, the tether broke, melted, or failed somehow, but collected data demonstrated potential for power generation.) 2. Griﬃths 7.8 3. The alternator in a car consists of a rectangular coil with 250 turns of wire and area 0.01 m 2 rotating in a 0.1 T magnetic ﬁeld. If the rotation rate is 1000 rpm, what is the peak output voltage? 4. Griﬃths 7.18 5. Griﬃths 7.20 6. Show the the mutual inductance of an inﬁnite wire and an equilateral triangle, as pictured below, is M = μ π √ 3 h ( a + b ) ln ± 1 + a b ²-a i (1) b a inﬁnitely long wire 7. Griﬃths 7.32 8. Griﬃths 7.50 (This problem will make you think twice about wiring meters into a circuit. Do you understand why the answer is what it is?) 9. Griﬃths 7.54 10. Griﬃths 7.58 1...
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