What is the effect of distance on magnetic forces between electromagnetic coils?

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SUMMARY

The discussion centers on the effects of distance on magnetic forces between two electromagnetic coils. It concludes that while a magnetic action force exists on one coil, the other coil does not experience an equal and opposite reaction due to the finite propagation speed of magnetic interactions. The conversation references Newton's third law and suggests the use of Lorentz transformations for a more accurate analysis of the forces involved when the coils are in relative motion.

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bstruss
I have attached a drawing that depicts the situation of two electromagetic coils in space separated by a vast distance. It seems to me that in this case there would be a magnetic action force on the right coil but no reaction on the left coil. I'm probably missing something here but I would appreciate any pointers on what that might be. If the description or graphic is unclear, please let me know.

Thanks!

Illustration
 
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Newton's third law (in fact, the force concept as such) only holds if the propagation speed of the interaction is infinite. I have examined a similar problem (a retarded interaction when the objects are moving relatively to each other) on my webpage http://www.physicsmyths.org.uk/retard.htm.
 
Thomas, may be you need to use Lorents transformations (instead of Galilean) between systems?
 

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