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Electrostatics physics help

  1. Feb 26, 2007 #1
    Well,I think this is interesting.I invite people to think over it.
    consider a charged spherical shell.Throughout its interior,E=0.
    Now,consider the centre.From Laplace's equation and Earnshaw's theorem,this point is not a point of potential minimum.So,a charge at this point cannot be in stable equilibrium.Say,you displace it slightly.
    What do you find.It just gets stagnant where you left it!
    If this is not a point of stable eqlbm,it is not also a point of unstable equilibrium.
    So,is it a point of neutral equilibrium?
    Apparently seems so.But,I wish to confirm.
  2. jcsd
  3. Feb 26, 2007 #2

    Claude Bile

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    Why not?

  4. Feb 26, 2007 #3
    if you displace it slightly, that is, if you nudge it: it will keep moving in that direction, eventually leaving the interior. Seems unstable.
  5. Feb 26, 2007 #4
    While it is the lowest value the potential can have, it doesn't have to count as stable equilibrium because the function is not derivable, and it's not a local minimum.
  6. Feb 26, 2007 #5


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    I'm not sure the premise is set up correctly: If the sphere is _empty_, then yes E=0. But now there's some E once the charge is inserted.
  7. Feb 27, 2007 #6


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    The center is not a point of minimum potential simply because the field is 0 throughout the sphere. Every point in the interior of the sphere is a point of "neutral equilibrium". What's so strange about that?
  8. Feb 27, 2007 #7
    I agree with HallsofIvy:
    However,think of the case,where you have a sphere on which charge can move.Say,a conductor.As you move the charge inside,the surface charge distribution may be affected.Then,what would be the conclusion?
  9. Feb 27, 2007 #8
    You would be dealing with an electrodynamics. However, the time it takes for the system to return to the electrostatic limit is extremely short.
  10. Feb 28, 2007 #9
    However,I found it.The resulting case will be unstable equilibrium.
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