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An astronaut is connected to her spacecraft by a 25-m-long tether cord as she and the spacecraft orbit Earth in a circular path at a speed of $3.0 \times 10^{3} \mathrm{m} / \mathrm{s}$ . At one instant, the voltage measured between the ends of a wire embedded in the cord is measured to be 0.45 $\mathrm{V}$ . Assume the long dimension of the cord is perpendicular to the vertical component of Earth's magnetic field at that instant. (a) What is the magnitude of the vertical component of Earth's field at this location? (b) Does the measured voltage change as the system moves from one location to another? Explain.

a. 6.0 \mu T

b. \text { Yes }

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We're told that an astronaut is connected to a spacecraft by accord with a length L of 25 meters and that the spacecraft orbits Earth at a speed V of three times senator third meters per second. At one instance, the vaulted measure between the end of the wire embedded in the cord is measured to be 0.45 volts to the induced E. M F 0.45 volts. So assume the long dimensions of the court are perpendicular to the verdict components of the Earth's magnetic field. So a what is the magnitude of the vertical component of the Earth's magnetic field at this location? So for part A, we can use the fact that the induce cmf uh, here for this magnetic field is equal to the magnitude of the magnetic field times the length of the court times, the velocity of movement. Therefore, the magnetic field is equal to the induced E m f, divided by the length times, the velocity plugging those values. In this expression, we find a value for the magnetic field of six times 10 to the minus six Tesla, so you can leave it a six times 10 to the minus six Tesla, Or this is also six Micro Tesla's. We'll just leave it like this and box in the solution for part A now Part B says, does the measured voltage change As the system moves from one location to another? Some will indicate this is part B. So the answer to this is gonna be yes. When the system or the spacecraft in the quarter is moving from one location to the other. The measured voltage at the end of the court will be changed from one location to the other because the angle made by the long side of the cord with the vertical component of Earth's magnetic field will change. So it says yes and explain yourself So we'll say yes, because the angle made by the long side of the corps with we need a little bit more space here with Earth's with the vertical component. Actually with the vertical component of Earth's magnetic field, we'll just call that Byfield changes, And so, since that angle is changing, the value will change. This is all boxed in as the solution for Part B