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Electromagnetic induction is the production of voltage across a conductor moving through a magnetic field.

Since an orbiting satellite is passing through the Earth's magnetic field would a voltage be induced in a conductor inside the satellite?

I would expect this voltage to be incredibly small but if true where is this energy "coming from"?

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This is sort of a dupe of physics.stackexchange.com/questions/651/… –  nibot Nov 20 '10 at 0:45
This is where I wish there was a subquestion feature of SE sites. If electricity can be generated from satelittes then would this eventually decrease the earths magnetic field strength, or slow the spin of the Earth (if the satellite had no velocity and it was the Earth that was moving under it) –  Jonathan. Nov 20 '10 at 21:44
@Jonathan. You could simply link to the question instead ... –  Everyone Jul 12 '12 at 18:34
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3 Answers

From the kinetic energy of the satellite -- this will make it eventually fall on the Earth surface.

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So a voltage would be induced? How could this be calculated? –  aaronfarr Nov 19 '10 at 21:30
It depends on the relative orientation of the objects/fields involved, but basically the voltage is related to the product of the length of the conductor, its speed, and the strength of the magnetic field. –  David Z Nov 19 '10 at 21:46
@aaronfarr As David mentioned, by third Maxwell equation (en.wikipedia.org/wiki/Faraday's_law_of_induction); yet there will be the problem with magnetic field, it is quite nonlinear and it is hard to find some details. –  mbq Nov 19 '10 at 22:23
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NASA actually experimented with producing current in tethers suspended from the space shuttle. The current generated was sufficient to melt the tether.

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In the case of the satellite, there is virtually no power being dissipated so there is no energy being taken from anywhere. When the moving satellite (i.e. conductor) first enters the magnetic field, an electric field is indeed induced, and this causes charge of opposite signs to build on opposite sides of the satellite which quickly creates an opposing electric field, and current ceases to flow.

IF, however, this excess of charge were used to produce current and somehow continuously extract power, then the replenishing of that excess charge would mean a continuous current across the satellite. This would then interact with the magnetic field to produce a force which (by Lenz's law) opposes the satellite's motion and slows it down. Thus, any power generated is drawn from the satellite's orbital energy.

The space shuttle tethers referred to by Humble work like this: current is made to flow across the "satellite" (i.e. the shuttle and the tether), and the excess charge on either end is dissipated through the ionosphere. This explains another important feature: to draw power from the orbital energy you need a net current through the satellite, which is impossible to do with a closed system due to conservation of charge, and like the shuttle you need some external way of dealing with the excess charge.

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It would produce a force against what exactly? It's in a vacuum (the Earth magnetic field extends beyond the upper atmosphere), so what would this created force react against? –  Jonathan. May 1 '12 at 16:51
@Johnathan: it's in a vacuum, of course, but it is also interacting magnetically with the Earth's core (or else nothing would happen). The lost momentum is transiently absorbed into the magnetic field and then into the currents inside the Earth's core which created the magnetic field in the first place. –  Emilio Pisanty May 1 '12 at 19:31
(also, the shuttle in particular is not exactly in a vacuum, since the ionosphere is used to drain excess charge from the ends of the wire. This means that there is some small net current (widely dispersed) throughout the ionosphere, which causes a resultant force in the direction of the satellite's motion. One can then see the effect as transferring orbital energy to some device on board and orbital momentum to the ionosphere.) –  Emilio Pisanty May 1 '12 at 19:34
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