What if we charge an uncharged sphere by making contact with sphere bearing 3 electrons charge Suppose say we have 2 identical conducting spheres. Then we have removed 3 electrons from one of the sphere. Now how will charge distribute on each sphere after charging the uncharged sphere by conduction.  Charging by conduction involves the contact of a charged object to a neutral object. In this process both spheres will reach a common potential. Then how the 3rd electron distribute on each sphere after they are separated? Will it break into smaller components or it is projected away from both the spheres or it remains in the mid-way between those spheres?
 A: As some comments suggest, the electric potential on the +3 sphere is not going to be uniform; the three holes will probably be moving all over the place.
The other obvious thing is that, after separating the two spheres, there is a probability distribution that the 3 holes will be [0,3], [1,2], [2,1],[3,0] . My offhand guess is that these cases will turn out to be equiprobable but I'll leave the analysis to someone who actually survived their encounter with Jackson's book.
A: To be honest, nobody can tell for sure, as it's all just a matter of probabilities, and so I'll concentrate on the "more probable" outcomes.
The electron will never "break into smaller components". Charge only exists in countable units, and an electron carries just one negative unit charge. There is no half-electron carrying half the charge.
The third electron will end up in one of the spheres. Both versions are equally probable:

*

*Two of the three electrons end up in sphere A, and one in B.

*One electron ends up in A, and two in B.

Less probable, but not at all impossible, are configurations like e.g.:

*

*None in A, all three in B.

*A gets the three electrons, plus one free electron that moved from B to A.

In a simplified model, you can understand the electrons as constantly moving around irregularly, so that temporarily there can be quite some inbalance between the charges on A and B. And if you separate the spheres then, the inbalance is persisted, as the electrons won't cross the non-conductive gap between the spheres (or: with such a small probability that we ignore that).
