Electrostatics: "Compressing" Charged Spherical Shell

  • #26
TSny
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Interesting; intuitively I would have said less work was involved in b), but it appears that it is the same to the first order of approximation, less to a second order.
Your intuition seems good to me in that it would take less work in part b for a finite change in r.
 
  • #27
haruspex
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May I know what you mean when you say "uneasy"?
It's because the thing being moved is also contributing to the force.
E.g., consider instead a large flat plate being moved along a normal to itself. No work would be done in this case. Maybe I'm missing a key aspect to your argument, and that this would resolve the paradox.
Do I do this by using say, ##W = \frac{1}{2} \int_{s} \sigma V \ da## to calculate potential energy of a sphere with radius ##r##, then ##r-dr##, then taking the their difference (in both parts)?
Yes, but as TSny points out you also have to add the PE of the charge that moves into the constant voltage reservoir in part b. I.e. figure out how much less charge the reduced sphere would have, and add the energy required to bring that from infinity into the reservoir.
 

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