Potential energy of a shell and a disc, both covered uniformly with charge

[Gursimran Singh]

Homework Statement

A thin disc of radius R is held closing the opening of a thin hemispherical shell of the same radius. Both the bodies are made of insulating materials and have uniform charges of surface charge density Sigma each. The plate is released with shell fixed. Find maximum kinetic energy of plate after being released?

Relevant Equations

PE = k(q1)(q2)/r

Double integration maybe?? I calculated potential due to shell on plate's center but not on other points on it's surface.

 

[TSny]

I find it hard to give a hint for this problem without destroying the "ah ha!". Forget any integration.

I found it helpful to think about the work I'd have to do to bring the disk in from infinity in order to cap the hemisphere.

 

[TSny]

A bit more help:

Spoiler

Try to replace the hemispherical distribution of charge with a different geometrical distribution such that it would be easier to determine the potential energy of the disk and such that it might help in determining the potential energy for the hemispherical case.