E9M.5 NASA has investigated using an \"electromagnetic tether\" as a possible pr

Question

E9M.5 NASA has investigated using an "electromagnetic tether" as a possible propulsion system for satellites in low earth orbit. The basic idea involves stringing a vertical cable between two satellites orbiting the earth. The lower satellite has a power supply that collects electrons from the tenuous plasma in the upper ionosphere and drives them through the tether cable to the satellite at the other end, which then emits the electrons back into the ionosphere. The earth's magnetic field exerts a force on the current flowing through the tether. Such a force can help the sys- tem maneuver or simply keep it orbiting in spite of the drag forces (from the ionosphere) that would otherwise cause it to lose altitude. Assume (for the sake of simplicity) that the tether system orbits in the earth's equatorial plane. The drawing below then shows the situation as viewed from a vantage point above the earth's north pole. Tether Satellites Earth Wwill the magnetic force on the tether as depicted above act to increase or decrease the system's speed?

Explanation / Answer

a. from the figure we can see

the electrons are moving upwards inthe wire, so the conventional current flows downwards

the magnetic field is out of the page

hence form the left hand rule , the magnetic force on the wire is towards the left

as depicted the intial velocity is towards the left, so this force will speed up the system

b. given, altitide of the system of satellites, h = 200,000 m

current in the tether, i = 1 A

length of tether, l = 500 m

radius of earth, R = 6371,000 m

mass of earth, M = 5.972*10^24 kg

so let speed of the system be v

then

GM/(R + h) = v^2

v = sqrt(6.67*10^-11*5.972*10^24/(6371,000 + 200,000))

v = 7785.868 m/s

now, magnetic fioeld of earth = 5*10^-5 T

then net force on the wire F = Bil = 5*10^-5*1*500 = 0.025 N

rate at which magentic field does work on the system = F*v = 194.6467 W

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