#### Problem:

In identical spherical droplets of water, each charged to the
same potential V, merge to form a larger droplet. What will be its
potential?

Solution:

- Concepts:

The potential of a spherically symmetric charge distribution of finite radius
R.
- Reasoning:

The potential at the surface of a spherically symmetric charge distribution is
V = kQ/R.

As we combine n drops, Q and R change.
- Details of the calculation:

We assume that initially the drops are very far apart, so that we can neglect
their interactions.

For one drop: V = kQ/R

For n drops: R --> R' = n^{(1/3)}R, Q --> Q' = nQ

V' = kQ'/R' = knQ/(n^{(1/3)}R) = n^{(2/3)}V.