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, $Q_1 + Q_2 = Q$.

The capacity depends on the material and geometry of your body. If is measured in Farad (F).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.