An astronaut is connected to her spacecraft by a 27 m long tether cord as she an

Question

An astronaut is connected to her spacecraft by a 27 m long tether cord as she and the spacecraft orbit Earth in a circular path at a speed of 3.1 times 10^3 m/s. At one instant, the voltage measured between the ends of a wire embedded in the cord is measured to be 0.42 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? Mu T (b) Does the measured voltage change as the system moves from one location to another? Explain.

Explanation / Answer

a) Since the motion is circular the angle between Earth's Magnetic Field and the velocity is 90 degrees.

Also the Equation for Voltage E=0.42 V induced in a wire of Length L=27 m by Magnetic Field B moving with velocity V =3.1 * 10^3 m/s at an
angle @ = 90 degrees is given by

E=BLVsin(@)
B=E/(LVsin(@))
= 0.42/(27*3.1*10^3*sin(90))
=5.017 uT

b)As long as the sytem follows the same circular path and the velocity and Earth's Magnetic Field do not change the measured voltage will remain the same.

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