Calculating Initial Potential and Heat of Metal Spheres Collision

[Salah93]

We have a metal sphere of radius R in the space and resistivity p. At a distance d>R from it we have antoher sphere of metal of radius r<<R and charge q. The 2 spheres intially are at rest.
What is the initial potential energy between them?
Now the sphere accelerate and collide anelastically. What is the amount of heat Q after this process?

P.S
This is NOT an homework, but an entrance exame at the university.
The question it's very intersting and i solved it.


For me is $$\frac{1}{4 \pi ε} \frac{q^2}{d}$$
and this is for the proprieties of metals.

 

[kuruman]

That looks about right and can be answered using the so called coefficients of potential. How would you answer the question about the heat generated? Hint: Assume that the small metal sphere is actually a point charge $q$ that becomes uniformly distributed over the surface of the large sphere after the collision.