# Homework Help: Tightening the charged sphere

1. Aug 16, 2014

### Dinheiro

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. Aug 16, 2014

### 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.

3. Aug 16, 2014

### 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.

4. Aug 17, 2014

### 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?