Breaking & building a charged hollow sphere

[xxhizors]

A charged hollow sphere with surface charge density $\sigma$ & radius R is cut into two hemispheres...certainly the hemispheres with equal charges on them would repel each other...Now a force is applied on both the hemispheres to align them again as the original sphere..i shall be highly thankful if u could assist me finding that force applied on each hemisphere...its not a homework assignment...just a question i saw in a book...!

 

[berkeman]

A charged hollow sphere with surface charge density $\sigma$ & radius R is cut into two hemispheres...certainly the hemispheres with equal charges on them would repel each other...Now a force is applied on both the hemispheres to align them again as the original sphere..i shall be highly thankful if u could assist me finding that force applied on each hemisphere...its not a homework assignment...just a question i saw in a book...!

Welcome to the PF.

Interesting problem. If they were point charges, what would be the repulsive force as a function of separation discance? Once the two hemispheres are no longer in contact, what will the (formerly uniform) charge distribution be?

 

[xxhizors]

How can we consider them as point charges in this problem...??
The repulsive force between the point charges can be calculated from coulomb's law...
I thought this about approaching this problem..

let us take a hemisphere & we try to build another on it and see the force of repulsion due to each infinitely small ring constituting the upper hemisphere on the lower one...
i can consider hemisphere to be build from infinite rings...