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Tightening the charged sphere

  1. Aug 16, 2014 #1
    1. The problem statement, all variables and given/known data
    A metal sphere, of radius R and cut in two along a plane whose minimum distance from sphere's centre is h, is uniformly charged by a total electric charge Q. What force is necessary to hold the two parts of the sphere together?

    2. Relevant equations
    Elestrostatic equations

    3. The attempt at a solution
    After the cut, the charges would get redistributed along the section, right? I figured a spherical cap repelling the other piece as they would get the same charge signal, so the neccessary force to hold them both is the repelling force F,
    F = EQ
    E is the electric field
    How can I calculate this E through the spherical cap??
  2. jcsd
  3. Aug 16, 2014 #2

    rude man

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    I wouldn't think in terms of an actual cut. The two quasi-hemispherical sections are joined together so all the charge is on the joined sphere's round surface, but there is a repulsive force trying to separate the two sections.
    Beyond that I have no hints to offer.
  4. Aug 16, 2014 #3
    Good call, as the force gets the quasi-hemisferical sections together, the charges will remain in the sphere's surface. I will retry it later.
  5. Aug 17, 2014 #4

    rude man

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    Good luck with this, I suspect it's a tough problem, probably belongs in the advanced physics forum.

    WAG: there's a line thru the center of the sphere and perpendicular to the cut. For each sphere section there's a point on this line where the net force in the direction of the line is zero (taking one section at a time). If you were to put the respective surface charges Q1 and Q2 at those two points, could you argue F = k Q1 Q2/d^2 where d is the distance separating those two points?
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