A water drop in electrostatic orbit around a needle in 0𝑔pic.twitter.com/G2x3Ud195K
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F ~ 1/r^3 does not admit a truly stable orbit, although maybe you could get a few periods of marginal stability.
+ Coulomb's law --> orbit
is there a charge distribution of the needle that could give a stable orbit?
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That's a good question, but I suspect that the answer is no, since both extreme cases (point charge and uniform line charge) are unstable. Of course, if the water drop has a net charge then you immediately get stability.
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hmm.. the motion to me doesn't look totally stable and i don't know the natural trajectories of the 1/r^3 1/r^5 potentials
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