Question
If a current flows in the Satellite Tether shown in Figure 23.12, use Faraday’s law, Lenz’s law, and RHR-1 to show that there is a magnetic force on the tether in the direction opposite to its velocity.
<b>Figure 23.12</b> Motional emf as electrical power conversion for the space shuttle is the motivation for the Tethered Satellite experiment. A 5 kV emf was predicted to be induced in the 20 km long tether while moving at orbital speed in the Earth’s magnetic field. The circuit is completed by a return path through the stationary ionosphere.
Figure 23.12 Motional emf as electrical power conversion for the space shuttle is the motivation for the Tethered Satellite experiment. A 5 kV emf was predicted to be induced in the 20 km long tether while moving at orbital speed in the Earth’s magnetic field. The circuit is completed by a return path through the stationary ionosphere.
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OpenStax College Physics for AP® Courses, Chapter 23, Problem 16 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. In 1992 and again in 1996, NASA did an experiment to try and create an emf using a tethered satellite that is tethered by a wire to the shuttle so this is the wire that connects the shuttle to the satellite. This black line here is something different; this is the return path for the circuit, the circuit being one that has current go up this wire to the satellite and then back through this ionosphere so the ionosphere is the ionized molecules that exist in the upper atmosphere of the Earth and so because the molecules are ionized or atoms are ionized, it conducts and so it's a bit of an unfamiliar experience but you can imagine that just you know, conduction happens through the air at that altitude. So what we have to show in this question is that there is a force pointing to the left in the opposite direction to the velocity on this tether. So first we have to figure out, why is this current happening in the first place? Well as the tether is released, the area enclosed by the tether and the return path through the ionosphere is going to be increasing as this wire gets longer and so because that area is increasing that means the flux is increasing and a change in flux induces an emf. So the flux will be increasing because of the greater area and so the induced current will produce a magnetic field that opposes that change and so since the flux is increasing into the page, the induced field will produce a magnetic field out of the page in order to oppose that increase in flux. And now if we grab this wire with our right hand and point our fingers out of the page in this loop so to speak, our thumb will be pointing upwards here or likewise if you grab this return path through the ionosphere, our thumb would be pointing down in any case, we have a counter-clockwise direction for the induced current. Okay! So now that the wire has a current going upwards, we can then apply the force due to a magnetic field on a current carrying wire. So our fingers will point into the page because that's the direction of the magnetic field, our thumb will point upwards since that's the direction of the current in the wire and our palm is in the direction of the force on the wire and our palm is pointing to the left. So there we go! This wire will experience a force to the left in the opposite direction to its velocity.