What Force Is Needed to Hold a Cut Charged Sphere Together?

[Dinheiro]

Homework Statement

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?

Homework Equations

Elestrostatic equations

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 necessary 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??

 

[rude man]

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.

 

[Dinheiro]

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.

 

[rude man]

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?