# In what ratio does the charge distribute if a charge and uncharged body touch each other?

Lets say a large charged body has $n$ elementary charges and is brought in contact with a small uncharged body. When the charge distributes, does it distribute in the ratio of number of atoms or each body gets half of the charge?

It depends on the capacities $C$ of the bodies. Say you have the charge $Q$ on body 1. That body has the capacity $C_1$. The second body has no charge ($Q_2 = 0$) and a capacity $C_2$. The charge will distribute so that the voltage of both bodies is the same. If the voltage is the same, there will be nothing that drives a current. If there is no current, the charge distribution is static.
Since $Q = CU$ (or as in american notation) $Q = CV$, you will have:
$$V_1 = V_2 \iff \frac{Q_1}{C_1} = \frac{Q_2}{C_2} \iff \frac{Q_1}{Q_2} = \frac{C_1}{C_2}.$$
$n$ elementary charges will make it $Q_1 = n e$. That charge has to split up. So you will have the above ratio and the charge conservation, $Q_1 + Q_2 = Q$.