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In one of NASA's space tether experiments, a 20.0 -km-long conducting wire was deployed by the space shuttle as it orbited at $7.86 \times 10^{3} \mathrm{m} / \mathrm{s}$ around Earth and across Earth's magnetic field lines. The resulting motional emf was used as a power source. If the component of Earth's magnetic field perpendicular to the tether was $1.50 \times 10^{-5} \mathrm{T}$ , determine the maximum possible potential difference between the two ends of the tether.

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Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Numerade Educator

University of Winnipeg

we're asked to determine the maximum possible potential difference between the two ends of a tether when the tether is 20 times 10 to the third meters long. Earth's magnetic field here is maximum of 1.5 times 10 to the minus five Tesla and the velocity of orbit here V is equal a 7.86 times 10 to the third meters per second. So the maximum possible potential difference. Here we'll go. Capital V is equal to the magnitude of the magnetic field times the length of the tender times the velocity which the spacecraft is moving. So, plugging those values into this expression, we simply find that the maximum potential is 2000 300 and 58. And the units here, of course, are volts. So we can go ahead and box set in is the solution to our question