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There is a conducting sphere $S_1$ of radius 'r' mounted on an insulating handle. The sphere is given a charge Q. Another uncharged conducting sphere $S_2$ of radius R mounted on an insulating handle is now brought in contact with S1 for sufficient time and then removed. $S_1$ is again given a charge Q and $S_2$ is again brought in contact with it and then removed. The process is repeated 'n'times. The purpose is to find the charge on $S_2$ after n times and for the special case where n tends to infinity.

However the solution does not considers the potential at the centre of $S_1$ due to $S_2$ and at the centre of $S_2$ due to $S_1$. Why?

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  • $\begingroup$ Hint:For every time the two spheres are brought in contact, their potentials equalize, on the first touch, $k(Q - q_1)R = kq_1r$ On the second touch, $k(Q - q_2)R = k(q_1 + q_2)r$ Now find a relation $\endgroup$
    – user212727
    Commented Jan 31, 2019 at 11:52
  • $\begingroup$ Why are you focused on the potential at the centre of the sphere? Can you elaborate? $\endgroup$
    – my2cts
    Commented Jan 31, 2019 at 12:56
  • $\begingroup$ When we consider redistribution of charges in this case, we distribute the charges such that potential of the two spheres is equal(so that there is no more charge flow. So in the expression shouldn't we consider the potential at the centre of one sphere due to another and vice versa? $\endgroup$
    – Shubham Singh
    Commented Feb 3, 2019 at 4:56

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