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My extension : What are all the factors that determine the new charge distribution?

What if they are connected by a metallic rod?

What if these two are insulator material? We are all told in the beginning texts that when you bring a charged body (could insulator or conductor) in contact with another neutral body, they share the charge. But I have been bugged with several questions in this context. (When this distribution will be equal and when will it be unequal?) What factors determine the final charge distribution. I have been searching every where but I could not get the complete answer.

And I came across this question, in a book and am curious to know the answer of this and extrapolations of this question.

What if they have same polarity but different amounts of charge say Q1 and Q2?

What if one of them is a metal and the other one is an insulator?

Basically, is there a single expalnation or equation which will answer all these questions?